Xiaolin Wu's line algorithm
You are encouraged to solve this task according to the task description, using any language you may know.
Implement the Xiaolin Wu's line algorithm as described in Wikipedia. This algorithm draw antialiased lines. See Bresenham's line algorithm for aliased lines.
ARM Assembly
<lang ARM Assembly>
/* ARM assembly Raspberry PI */ /* program xiaolin1.s */
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly for the routine affichageMess displayerror see at end oh this program the instruction include */
/* REMARK 2 : display use a FrameBuffer device : see raspberry pi FrameBuffer documentation
this solution write directly on the screen of raspberry pi
other solution is to use X11 windows but X11 has a function drawline !! */
/* REMARK 3 : this program do not respect the convention for use, save and restau registers
in rhe routine call !!!! */
/*******************************************/ /* Constantes */ /*******************************************/ .equ STDOUT, 1 @ Linux output console .equ EXIT, 1 @ Linux syscall .equ WRITE, 4 @ Linux syscall .equ OPEN, 5 .equ CLOSE, 6 .equ IOCTL, 0x36 .equ MMAP, 0xC0 .equ UNMAP, 0x5B .equ O_RDWR, 0x0002 @ open for reading and writing .equ MAP_SHARED, 0x01 @ Share changes. .equ PROT_READ, 0x1 @ Page can be read. .equ PROT_WRITE, 0x2 @ Page can be written.
/*******************************************/ /* Initialized data */ /*******************************************/ .data szMessErreur: .asciz "File open error.\n" szMessErreur1: .asciz "File close error.\n" szMessErreur2: .asciz "File mapping error.\n" szMessDebutPgm: .asciz "Program start. \n" szMessFinOK: .asciz "Normal end program. \n" szMessErrFix: .asciz "Read error info fix framebuffer \n" szMessErrVar: .asciz "Read error info var framebuffer \n" szRetourligne: .asciz "\n" szParamNom: .asciz "/dev/fb0" @ FrameBuffer device name szLigneVar: .ascii "Variables info : " sWidth: .fill 11, 1, ' '
.ascii " * "
sHeight: .fill 11, 1, ' '
.ascii " Bits par pixel : "
sBits: .fill 11, 1, ' '
.asciz "\n"
/*************************************************/ szMessErr: .ascii "Error code hexa : " sHexa: .space 9,' '
.ascii " decimal : "
sDeci: .space 15,' '
.asciz "\n"
.align 4 /* codes fonction pour la récupération des données fixes et variables */ FBIOGET_FSCREENINFO: .int 0x4602 @ function code for read infos fixes Framebuffer FBIOGET_VSCREENINFO: .int 0x4600 @ function code for read infos variables Framebuffer
/*******************************************/ /* UnInitialized data */ /*******************************************/ .bss .align 4 fix_info: .skip FBFIXSCinfo_fin @ memory reserve for structure FSCREENINFO .align 4 var_info: .skip FBVARSCinfo_fin @ memory reserve for structure VSCREENINFO /**********************************************/ /* -- Code section */ /**********************************************/ .text .global main
main:
ldr r0,iAdrszMessDebutPgm bl affichageMess @ display message ldr r0,iAdrszParamNom @ frameBuffer device name mov r1,#O_RDWR @ flags read/write mov r2,#0 @ mode mov r7,#OPEN @ open device FrameBuffer svc 0 cmp r0,#0 @ error ? ble erreur mov r10,r0 @ save FD du device FrameBuffer in r10 ldr r1,iAdrFBIOGET_VSCREENINFO @ read variables datas of FrameBuffer ldr r1,[r1] @ load code function ldr r2,iAdrvar_info @ structure memory address mov r7, #IOCTL @ call system swi 0 cmp r0,#0 blt erreurVar ldr r2,iAdrvar_info ldr r0,[r2,#FBVARSCinfo_xres] @ load screen width ldr r1,iAdrsWidth @ and convert in string for display bl conversion10S ldr r0,[r2,#FBVARSCinfo_yres] @ load screen height ldr r1,iAdrsHeight @ and convert in string for display bl conversion10S ldr r0,[r2,#FBVARSCinfo_bits_per_pixel] @ load bits by pixel ldr r1,iAdrsBits @ and convert in string for display bl conversion10S ldr r0,iAdrszLigneVar @ display result bl affichageMess
mov r0,r10 @ FD du FB ldr r1,iAdrFBIOGET_FSCREENINFO @ read fixes datas of FrameBuffe ldr r1,[r1] @ load code function ldr r2,iAdrfix_info @ structure memory address mov r7, #IOCTL @ call system svc 0 cmp r0,#0 @ error ? blt erreurFix ldr r0,iAdrfix_info
ldr r1,iAdrfix_info @ read size memory for datas
ldr r1,[r1,#FBFIXSCinfo_smem_len] @ in octets
@ datas mapping
mov r0,#0
ldr r2,iFlagsMmap
mov r3,#MAP_SHARED
mov r4,r10
mov r5,#0
mov r7, #MMAP @ 192 call system for mapping
swi #0
cmp r0,#0 @ error ?
beq erreur2
mov r9,r0 @ save mapping address in r9
/*************************************/
/* display draw */
bl dessin
/************************************/
mov r0,r9 @ mapping close
ldr r1,iAdrfix_info
ldr r1,[r1,#FBFIXSCinfo_smem_len] @ mapping memory size
mov r7,#UNMAP @call system 91 for unmapping
svc #0 @ error ?
cmp r0,#0
blt erreur1
@ close device FrameBuffer
mov r0,r10 @ load FB du device
mov r7, #CLOSE @ call system
swi 0
ldr r0,iAdrszMessFinOK @ display end message
bl affichageMess
mov r0,#0 @ return code = OK
b 100f
erreurFix: @ display read error datas fix
ldr r1,iAdrszMessErrFix @ message address bl displayError @ call display mov r0,#1 @ return code = error b 100f
erreurVar: @ display read error datas var
ldr r1,iAdrszMessErrVar bl displayError mov r0,#1 b 100f
erreur: @ display open error
ldr r1,iAdrszMessErreur bl displayError mov r0,#1 b 100f
erreur1: @ display unmapped error
ldr r1,iAdrszMessErreur1 bl displayError mov r0,#1 b 100f
erreur2: @ display mapped error
ldr r1,iAdrszMessErreur2 bl displayError mov r0,#1 b 100f
100: @ end program
mov r7, #EXIT svc 0
/************************************/ iAdrszParamNom: .int szParamNom iFlagsMmap: .int PROT_READ|PROT_WRITE iAdrszMessErreur: .int szMessErreur iAdrszMessErreur1: .int szMessErreur1 iAdrszMessErreur2: .int szMessErreur2 iAdrszMessDebutPgm: .int szMessDebutPgm iAdrszMessFinOK: .int szMessFinOK iAdrszMessErrFix: .int szMessErrFix iAdrszMessErrVar: .int szMessErrVar iAdrszLigneVar: .int szLigneVar iAdrvar_info: .int var_info iAdrfix_info: .int fix_info iAdrFBIOGET_FSCREENINFO: .int FBIOGET_FSCREENINFO iAdrFBIOGET_VSCREENINFO: .int FBIOGET_VSCREENINFO iAdrsWidth: .int sWidth iAdrsHeight: .int sHeight iAdrsBits: .int sBits /***************************************************/ /* dessin */ /***************************************************/ /* r9 framebuffer memory address */ dessin:
push {r1-r12,lr} @ save registers
mov r0,#255 @ red
mov r1,#255 @ green
mov r2,#255 @ blue 3 bytes 255 = white
bl codeRGB @ code color RGB 32 bits
mov r1,r0 @ background color
ldr r0,iAdrfix_info @ load memory mmap size
ldr r0,[r0,#FBFIXSCinfo_smem_len]
bl coloriageFond @
/* draw line 1 */
mov r0,#200 @ X start line
mov r1,#200 @ Y start line
mov r2,#200 @ X end line
mov r3,#100 @ Y end line
ldr r4,iAdrvar_info
ldr r4,[r4,#FBVARSCinfo_xres] @ load screen width
bl drawLine
/* draw line 2 */
mov r0,#200
mov r1,#200
mov r2,#200
mov r3,#300
ldr r4,iAdrvar_info
ldr r4,[r4,#FBVARSCinfo_xres]
bl drawLine
/* draw line 3 */
mov r0,#200
mov r1,#200
mov r2,#100
mov r3,#200
ldr r4,iAdrvar_info
ldr r4,[r4,#FBVARSCinfo_xres]
bl drawLine
/* draw line 4 */
mov r0,#200
mov r1,#200
mov r2,#300
mov r3,#200
ldr r4,iAdrvar_info
ldr r4,[r4,#FBVARSCinfo_xres]
bl drawLine
/* draw line 5 */
mov r0,#200
mov r1,#200
mov r2,#100
mov r3,#100
ldr r4,iAdrvar_info
ldr r4,[r4,#FBVARSCinfo_xres]
bl drawLine
/* draw line 6 */
mov r0,#200
mov r1,#200
mov r2,#100
mov r3,#300
ldr r4,iAdrvar_info
ldr r4,[r4,#FBVARSCinfo_xres]
bl drawLine
/* draw line 7 */
mov r0,#200
mov r1,#200
mov r2,#300
mov r3,#300
ldr r4,iAdrvar_info
ldr r4,[r4,#FBVARSCinfo_xres]
bl drawLine
/* draw line 8 */
mov r0,#200
mov r1,#200
mov r2,#300
mov r3,#100
ldr r4,iAdrvar_info
ldr r4,[r4,#FBVARSCinfo_xres]
bl drawLine
100:
pop {r1-r12,lr} @ restaur registers
bx lr @ end function
/********************************************************/ /* set background color */ /********************************************************/ /* r0 contains size screen memory */ /* r1 contains rgb code color */ /* r9 contains screen memory address */ coloriageFond:
push {r2,lr}
mov r2,#0 @ counter
1: @ begin loop
str r1,[r9,r2]
add r2,#4
cmp r2,r0
blt 1b
pop {r2,lr}
bx lr
/********************************************************/ /* Xiaolin Wu line algorithm */ /* no floating point compute, multiply value for 128 */ /* for integer compute */ /********************************************************/ /* r0 x1 start line */ /* r1 y1 start line */ /* r2 x2 end line */ /* r3 y2 end line */ /* r4 screen width */ drawLine:
push {fp,lr} @ save registers ( no other registers save )
mov r5,r0 @ save x1
mov r6,r1 @ save y1
cmp r2,r5 @ compar x2,x1
subgt r1,r2,r5
suble r1,r5,r2 @ compute dx=abs val de x1-x2
cmp r3,r6 @ compar y2,y1
subgt r0,r3,r6
suble r0,r6,r3 @ compute dy = abs val de y1-y2
cmp r1,r0 @ compare dx , dy
blt 5f @ dx < dy
@ dx > dy
cmp r2,r5 @ compare x2,x1
movlt r8,r5 @ x2 < x1
movlt r5,r2 @ swap x2,x1
movlt r2,r8
movlt r8,r6 @ swap y2,y1
movlt r6,r3
movlt r3,r8
lsl r0,#7 @ * by 128
mov r7,r2 @ save x2
mov r8,r3 @ save y2
cmp r1,#0 @ divisor = 0 ?
moveq r10,#128
beq 1f
bl division @ gradient compute (* 128)
mov r10,r2 @ r10 contient le gradient
1:
@ display start points mov r0,#64 bl colorPixel mov r3,r0 @ RGB color mov r0,r5 @ x1 mov r1,r6 @ y1 mov r2,r4 @ screen witdh bl aff_pixel_codeRGB32 @ display pixel add r1,#1 @ increment y1 bl aff_pixel_codeRGB32 @ display end points mov r0,r7 @ x2 mov r1,r8 @ y2 bl aff_pixel_codeRGB32 add r1,#1 @ increment y2 bl aff_pixel_codeRGB32 cmp r8,r6 @ compar y2,y1 blt 3f @ y2 < y1 mov r4,r5 @ x = x1 lsl r5,r6,#7 @ compute y1 * 128 add r5,r10 @ compute intery = (y1 * 128 + gradient * 128)
2: @ start loop draw line pixels
lsr r1,r5,#7 @ intery / 128 = y lsl r8,r1,#7 sub r6,r5,r8 @ reminder of intery /128 = brightness mov r0,r6 bl colorPixel @ compute rgb color brightness mov r3,r0 @ rgb color mov r0,r4 @ x bl aff_pixel_codeRGB32 @ display pixel 1 add r1,#1 @ increment y rsb r0,r6,#128 @ compute 128 - brightness bl colorPixel @ compute new rgb color mov r3,r0 mov r0,r4 bl aff_pixel_codeRGB32 @ display pixel 2 add r5,r10 @ add gradient to intery add r4,#1 @ increment x cmp r4,r7 @ x < x2 ble 2b @ yes -> loop b 100f @ else end
3: @ y2 < y1
mov r4,r7 @ x = x2 mov r7,r5 @ save x1 lsl r5,r8,#7 @ y = y1 * 128 add r5,r10 @ compute intery = (y1 * 128 + gradient * 128)
4:
lsr r1,r5,#7 @ y = ent(intery / 128) lsl r8,r1,#7 sub r8,r5,r8 @ brightness = remainder mov r0,r8 bl colorPixel mov r3,r0 mov r0,r4 bl aff_pixel_codeRGB32 add r1,#1 rsb r0,r8,#128 bl colorPixel mov r3,r0 mov r0,r4 bl aff_pixel_codeRGB32 add r5,r10 sub r4,#1 @ decrement x cmp r4,r7 @ x > x1 bgt 4b @ yes -> loop b 100f
5: @ dx < dy
cmp r3,r6 @ compare y2,y1 movlt r8,r5 @ y2 < y1 movlt r5,r2 @ swap x1,x2 movlt r2,r8 movlt r8,r6 @ swap y1,y2 movlt r6,r3 movlt r3,r8 mov r8,r1 @ swap r0,r1 for routine division mov r1,r0 lsl r0,r8,#7 @ dx * by 128 mov r7,r2 @ save x2 mov r8,r3 @ save y2 cmp r1,#0 @ dy = zero ? moveq r10,#128 beq 6f bl division @ compute gradient * 128 mov r10,r2 @ gradient -> r10
6:
@ display start points mov r0,#64 bl colorPixel mov r3,r0 @ color pixel mov r0,r5 @ x1 mov r1,r6 @ y1 mov r2,r4 @ screen width bl aff_pixel_codeRGB32 add r1,#1 bl aff_pixel_codeRGB32 @ display end points mov r0,r7 mov r1,r8 bl aff_pixel_codeRGB32 add r1,#1 bl aff_pixel_codeRGB32 cmp r5,r7 @ x1 < x2 ? blt 8f mov r4,r6 @ y = y1 lsl r5,#7 @ compute x1 * 128 add r5,r10 @ compute interx
7:
lsr r1,r5,#7 @ compute x = ent ( interx / 128) lsl r3,r1,#7 sub r6,r5,r3 @ brightness = remainder mov r0,r6 bl colorPixel mov r3,r0 mov r0,r1 @ new x add r7,r0,#1 mov r1,r4 @ y bl aff_pixel_codeRGB32 rsb r0,r6,#128 bl colorPixel mov r3,r0 mov r0,r7 @ new x + 1 mov r1,r4 @ y bl aff_pixel_codeRGB32 add r5,r10 add r4,#1 cmp r4,r8 ble 7b b 100f
8:
mov r4,r8 @ y = y2 lsl r5,#7 @ compute x1 * 128 add r5,r10 @ compute interx
9:
lsr r1,r5,#7 @ compute x lsl r3,r1,#7 sub r8,r5,r3 mov r0,r8 bl colorPixel mov r3,r0 mov r0,r1 @ new x add r7,r0,#1 mov r1,r4 @ y bl aff_pixel_codeRGB32 rsb r0,r8,#128 bl colorPixel mov r3,r0 mov r0,r7 @ new x + 1 mov r1,r4 @ y bl aff_pixel_codeRGB32 add r5,r10 sub r4,#1 cmp r4,r6 bgt 9b b 100f
100:
pop {fp,lr}
bx lr
/********************************************************/ /* brightness color pixel */ /********************************************************/ /* r0 % brightness ( 0 to 128) */ colorPixel:
push {r1,r2,lr} /* save des 2 registres frame et retour */
cmp r0,#0
beq 100f
cmp r0,#128
mov r0,#127
lsl r0,#1 @ red = brightness * 2 ( 2 to 254)
mov r1,r0 @ green = red
mov r2,r0 @ blue = red
bl codeRGB @ compute rgb code color 32 bits
100:
pop {r1,r2,lr}
bx lr
/***************************************************/ /* display pixels 32 bits */ /***************************************************/ /* r9 framebuffer memory address */ /* r0 = x */ /* r1 = y */ /* r2 screen width in pixels */ /* r3 code color RGB 32 bits */ aff_pixel_codeRGB32:
push {r0-r4,lr} @ save registers
@ compute location pixel
mul r4,r1,r2 @ compute y * screen width
add r0,r0,r4 @ + x
lsl r0,#2 @ * 4 octets
str r3,[r9,r0] @ store rgb code in mmap memory
pop {r0-r4,lr} @ restaur registers
bx lr
/********************************************************/ /* Code color RGB */ /********************************************************/ /* r0 red r1 green r2 blue */ /* r0 returns RGB code */ codeRGB:
lsl r0,#16 @ shift red color 16 bits lsl r1,#8 @ shift green color 8 bits eor r0,r1 @ or two colors eor r0,r2 @ or 3 colors in r0 bx lr
/***************************************************/ /* ROUTINES INCLUDE */ /***************************************************/ .include "./affichage.inc"
/***************************************************/ /* DEFINITION DES STRUCTURES */ /***************************************************/ /* structure FSCREENINFO */ /* voir explication détaillée : https://www.kernel.org/doc/Documentation/fb/api.txt */
.struct 0
FBFIXSCinfo_id: /* identification string eg "TT Builtin" */
.struct FBFIXSCinfo_id + 16
FBFIXSCinfo_smem_start: /* Start of frame buffer mem */
.struct FBFIXSCinfo_smem_start + 4
FBFIXSCinfo_smem_len: /* Length of frame buffer mem */
.struct FBFIXSCinfo_smem_len + 4
FBFIXSCinfo_type: /* see FB_TYPE_* */
.struct FBFIXSCinfo_type + 4
FBFIXSCinfo_type_aux: /* Interleave for interleaved Planes */
.struct FBFIXSCinfo_type_aux + 4
FBFIXSCinfo_visual: /* see FB_VISUAL_* */
.struct FBFIXSCinfo_visual + 4
FBFIXSCinfo_xpanstep: /* zero if no hardware panning */
.struct FBFIXSCinfo_xpanstep + 2
FBFIXSCinfo_ypanstep: /* zero if no hardware panning */
.struct FBFIXSCinfo_ypanstep + 2
FBFIXSCinfo_ywrapstep: /* zero if no hardware ywrap */
.struct FBFIXSCinfo_ywrapstep + 4
FBFIXSCinfo_line_length: /* length of a line in bytes */
.struct FBFIXSCinfo_line_length + 4
FBFIXSCinfo_mmio_start: /* Start of Memory Mapped I/O */
.struct FBFIXSCinfo_mmio_start + 4
FBFIXSCinfo_mmio_len: /* Length of Memory Mapped I/O */
.struct FBFIXSCinfo_mmio_len + 4
FBFIXSCinfo_accel: /* Indicate to driver which specific chip/card we have */
.struct FBFIXSCinfo_accel + 4
FBFIXSCinfo_capabilities: /* see FB_CAP_* */
.struct FBFIXSCinfo_capabilities + 4
FBFIXSCinfo_reserved: /* Reserved for future compatibility */
.struct FBFIXSCinfo_reserved + 8
FBFIXSCinfo_fin:
/* structure VSCREENINFO */
.struct 0
FBVARSCinfo_xres: /* visible resolution */
.struct FBVARSCinfo_xres + 4
FBVARSCinfo_yres:
.struct FBVARSCinfo_yres + 4
FBVARSCinfo_xres_virtual: /* virtual resolution */
.struct FBVARSCinfo_xres_virtual + 4
FBVARSCinfo_yres_virtual:
.struct FBVARSCinfo_yres_virtual + 4
FBVARSCinfo_xoffset: /* offset from virtual to visible resolution */
.struct FBVARSCinfo_xoffset + 4
FBVARSCinfo_yoffset:
.struct FBVARSCinfo_yoffset + 4
FBVARSCinfo_bits_per_pixel: /* bits par pixel */
.struct FBVARSCinfo_bits_per_pixel + 4
FBVARSCinfo_grayscale: /* 0 = color, 1 = grayscale, >1 = FOURCC */
.struct FBVARSCinfo_grayscale + 4
FBVARSCinfo_red: /* bitfield in fb mem if true color, */
.struct FBVARSCinfo_red + 4
FBVARSCinfo_green: /* else only length is significant */
.struct FBVARSCinfo_green + 4
FBVARSCinfo_blue:
.struct FBVARSCinfo_blue + 4
FBVARSCinfo_transp: /* transparency */
.struct FBVARSCinfo_transp + 4
FBVARSCinfo_nonstd: /* != 0 Non standard pixel format */
.struct FBVARSCinfo_nonstd + 4
FBVARSCinfo_activate: /* see FB_ACTIVATE_* */
.struct FBVARSCinfo_activate + 4
FBVARSCinfo_height: /* height of picture in mm */
.struct FBVARSCinfo_height + 4
FBVARSCinfo_width: /* width of picture in mm */
.struct FBVARSCinfo_width + 4
FBVARSCinfo_accel_flags: /* (OBSOLETE) see fb_info.flags */
.struct FBVARSCinfo_accel_flags + 4
/* Timing: All values in pixclocks, except pixclock (of course) */ FBVARSCinfo_pixclock: /* pixel clock in ps (pico seconds) */
.struct FBVARSCinfo_pixclock + 4
FBVARSCinfo_left_margin:
.struct FBVARSCinfo_left_margin + 4
FBVARSCinfo_right_margin:
.struct FBVARSCinfo_right_margin + 4
FBVARSCinfo_upper_margin:
.struct FBVARSCinfo_upper_margin + 4
FBVARSCinfo_lower_margin:
.struct FBVARSCinfo_lower_margin + 4
FBVARSCinfo_hsync_len: /* length of horizontal sync */
.struct FBVARSCinfo_hsync_len + 4
FBVARSCinfo_vsync_len: /* length of vertical sync */
.struct FBVARSCinfo_vsync_len + 4
FBVARSCinfo_sync: /* see FB_SYNC_* */
.struct FBVARSCinfo_sync + 4
FBVARSCinfo_vmode: /* see FB_VMODE_* */
.struct FBVARSCinfo_vmode + 4
FBVARSCinfo_rotate: /* angle we rotate counter clockwise */
.struct FBVARSCinfo_rotate + 4
FBVARSCinfo_colorspace: /* colorspace for FOURCC-based modes */
.struct FBVARSCinfo_colorspace + 4
FBVARSCinfo_reserved: /* Reserved for future compatibility */
.struct FBVARSCinfo_reserved + 16
FBVARSCinfo_fin:
</lang>
AutoHotkey
<lang AutoHotkey>#SingleInstance, Force
- NoEnv
SetBatchLines, -1
pToken := Gdip_Startup() global pBitmap := Gdip_CreateBitmap(500, 500) drawLine(100,50,400,400) Gdip_SaveBitmapToFile(pBitmap, A_ScriptDir "\linetest.png") Gdip_DisposeImage(pBitmap) Gdip_Shutdown(pToken) Run, % A_ScriptDir "\linetest.png" ExitApp
plot(x, y, c) {
A := DecToBase(255 * c, 16) Gdip_SetPixel(pBitmap, x, y, "0x" A "000000")
}
- integer part of x
ipart(x) {
return x // 1
}
rnd(x) {
return ipart(x + 0.5)
}
- fractional part of x
fpart(x) {
if (x < 0)
return 1 - (x - floor(x))
return x - floor(x)
}
rfpart(x) {
return 1 - fpart(x)
}
drawLine(x0,y0,x1,y1) {
steep := abs(y1 - y0) > abs(x1 - x0)
if (steep) {
temp := x0, x0 := y0, y0 := temp
temp := x1, x1 := y1, y1 := temp
}
if (x0 > x1 then) {
temp := x0, x0 := x1, x1 := temp
temp := y0, y0 := y1, y1 := temp
}
dx := x1 - x0
dy := y1 - y0
gradient := dy / dx
; handle first endpoint
xend := rnd(x0)
yend := y0 + gradient * (xend - x0)
xgap := rfpart(x0 + 0.5)
xpxl1 := xend ; this will be used in the main loop
ypxl1 := ipart(yend)
if (steep) {
plot(ypxl1, xpxl1, rfpart(yend) * xgap)
plot(ypxl1+1, xpxl1, fpart(yend) * xgap)
}
else {
plot(xpxl1, ypxl1 , rfpart(yend) * xgap)
plot(xpxl1, ypxl1+1, fpart(yend) * xgap)
}
intery := yend + gradient ; first y-intersection for the main loop
; handle second endpoint
xend := rnd(x1)
yend := y1 + gradient * (xend - x1)
xgap := fpart(x1 + 0.5)
xpxl2 := xend ;this will be used in the main loop
ypxl2 := ipart(yend)
if (steep) {
plot(ypxl2 , xpxl2, rfpart(yend) * xgap)
plot(ypxl2+1, xpxl2, fpart(yend) * xgap)
}
else {
plot(xpxl2, ypxl2, rfpart(yend) * xgap)
plot(xpxl2, ypxl2+1, fpart(yend) * xgap)
}
; main loop
while (x := xpxl1 + A_Index) < xpxl2 {
if (steep) {
plot(ipart(intery) , x, rfpart(intery))
plot(ipart(intery)+1, x, fpart(intery))
}
else {
plot(x, ipart (intery), rfpart(intery))
plot(x, ipart (intery)+1, fpart(intery))
}
intery := intery + gradient
}
}
DecToBase(n, Base) {
static U := A_IsUnicode ? "w" : "a"
VarSetCapacity(S,65,0)
DllCall("msvcrt\_i64to" U, "Int64",n, "Str",S, "Int",Base)
return, S
}</lang>
BBC BASIC
<lang bbcbasic> PROCdrawAntiAliasedLine(100, 100, 600, 400, 0, 0, 0)
END
DEF PROCdrawAntiAliasedLine(x1, y1, x2, y2, r%, g%, b%)
LOCAL dx, dy, xend, yend, grad, yf, xgap, ix1%, iy1%, ix2%, iy2%, x%
dx = x2 - x1
dy = y2 - y1
IF ABS(dx) < ABS(dy) THEN
SWAP x1, y1
SWAP x2, y2
SWAP dx, dy
ENDIF
IF x2 < x1 THEN
SWAP x1, x2
SWAP y1, y2
ENDIF
grad = dy / dx
xend = INT(x1 + 0.5)
yend = y1 + grad * (xend - x1)
xgap = xend + 0.5 - x1
ix1% = xend
iy1% = INT(yend)
PROCplot(ix1%, iy1%, r%, b%, g%, (INT(yend) + 1 - yend) * xgap)
PROCplot(ix1%, iy1% + 1, r%, b%, g%, (yend - INT(yend)) * xgap)
yf = yend + grad
xend = INT(x2 + 0.5)
yend = y2 + grad * (xend - x2)
xgap = x2 + 0.5 - xend
ix2% = xend
iy2% = INT(yend)
PROCplot(ix2%, iy2%, r%, b%, g%, (INT(yend) + 1 - yend) * xgap)
PROCplot(ix2%, iy2% + 1, r%, b%, g%, (yend - INT(yend)) * xgap)
FOR x% = ix1% + 1 TO ix2% - 1
PROCplot(x%, INT(yf), r%, b%, g%, INT(yf) + 1 - yf)
PROCplot(x%, INT(yf) + 1, r%, b%, g%, yf - INT(yf))
yf += grad
NEXT
ENDPROC
DEF PROCplot(X%, Y%, R%, G%, B%, a)
LOCAL C%
C% = TINT(X%*2,Y%*2)
COLOUR 1, R%*a + (C% AND 255)*(1-a), \
\ G%*a + (C% >> 8 AND 255)*(1-a), \
\ B%*a + (C% >> 16 AND 255)*(1-a)
GCOL 1
LINE X%*2, Y%*2, X%*2, Y%*2
ENDPROC</lang>
C
This implementation follows straightforwardly the pseudocode given on Wikipedia. (Further analysis of the code could give suggestions for improvements).
<lang c>void draw_line_antialias(
image img,
unsigned int x0, unsigned int y0,
unsigned int x1, unsigned int y1,
color_component r,
color_component g,
color_component b );</lang>
<lang c>inline void _dla_changebrightness(rgb_color_p from, rgb_color_p to, float br) {
if ( br > 1.0 ) br = 1.0; /* linear... Maybe something more complex could give better look */ to->red = br * (float)from->red; to->green = br * (float)from->green; to->blue = br * (float)from->blue;
}
- define plot_(X,Y,D) do{ rgb_color f_; \
f_.red = r; f_.green = g; f_.blue = b; \ _dla_plot(img, (X), (Y), &f_, (D)) ; }while(0)
inline void _dla_plot(image img, int x, int y, rgb_color_p col, float br) {
rgb_color oc; _dla_changebrightness(col, &oc, br); put_pixel_clip(img, x, y, oc.red, oc.green, oc.blue);
}
- define ipart_(X) ((int)(X))
- define round_(X) ((int)(((double)(X))+0.5))
- define fpart_(X) (((double)(X))-(double)ipart_(X))
- define rfpart_(X) (1.0-fpart_(X))
- define swap_(a, b) do{ __typeof__(a) tmp; tmp = a; a = b; b = tmp; }while(0)
void draw_line_antialias(
image img, unsigned int x1, unsigned int y1, unsigned int x2, unsigned int y2, color_component r, color_component g, color_component b )
{
double dx = (double)x2 - (double)x1;
double dy = (double)y2 - (double)y1;
if ( fabs(dx) > fabs(dy) ) {
if ( x2 < x1 ) {
swap_(x1, x2);
swap_(y1, y2);
}
double gradient = dy / dx;
double xend = round_(x1);
double yend = y1 + gradient*(xend - x1);
double xgap = rfpart_(x1 + 0.5);
int xpxl1 = xend;
int ypxl1 = ipart_(yend);
plot_(xpxl1, ypxl1, rfpart_(yend)*xgap);
plot_(xpxl1, ypxl1+1, fpart_(yend)*xgap);
double intery = yend + gradient;
xend = round_(x2); yend = y2 + gradient*(xend - x2); xgap = fpart_(x2+0.5); int xpxl2 = xend; int ypxl2 = ipart_(yend); plot_(xpxl2, ypxl2, rfpart_(yend) * xgap); plot_(xpxl2, ypxl2 + 1, fpart_(yend) * xgap);
int x;
for(x=xpxl1+1; x < xpxl2; x++) {
plot_(x, ipart_(intery), rfpart_(intery));
plot_(x, ipart_(intery) + 1, fpart_(intery));
intery += gradient;
}
} else {
if ( y2 < y1 ) {
swap_(x1, x2);
swap_(y1, y2);
}
double gradient = dx / dy;
double yend = round_(y1);
double xend = x1 + gradient*(yend - y1);
double ygap = rfpart_(y1 + 0.5);
int ypxl1 = yend;
int xpxl1 = ipart_(xend);
plot_(xpxl1, ypxl1, rfpart_(xend)*ygap);
plot_(xpxl1 + 1, ypxl1, fpart_(xend)*ygap);
double interx = xend + gradient;
yend = round_(y2); xend = x2 + gradient*(yend - y2); ygap = fpart_(y2+0.5); int ypxl2 = yend; int xpxl2 = ipart_(xend); plot_(xpxl2, ypxl2, rfpart_(xend) * ygap); plot_(xpxl2 + 1, ypxl2, fpart_(xend) * ygap);
int y;
for(y=ypxl1+1; y < ypxl2; y++) {
plot_(ipart_(interx), y, rfpart_(interx));
plot_(ipart_(interx) + 1, y, fpart_(interx));
interx += gradient;
}
}
}
- undef swap_
- undef plot_
- undef ipart_
- undef fpart_
- undef round_
- undef rfpart_
</lang>
C++
<lang c++>
- include <functional>
- include <algorithm>
- include <utility>
void WuDrawLine(float x0, float y0, float x1, float y1,
const std::function<void(int x, int y, float brightess)>& plot) {
auto ipart = [](float x) -> int {return int(std::floor(x));};
auto round = [](float x) -> float {return std::round(x);};
auto fpart = [](float x) -> float {return x - std::floor(x);};
auto rfpart = [=](float x) -> float {return 1 - fpart(x);};
const bool steep = abs(y1 - y0) > abs(x1 - x0);
if (steep) {
std::swap(x0,y0);
std::swap(x1,y1);
}
if (x0 > x1) {
std::swap(x0,x1);
std::swap(y0,y1);
}
const float dx = x1 - x0;
const float dy = y1 - y0;
const float gradient = (dx == 0) ? 1 : dy/dx;
int xpx11;
float intery;
{
const float xend = round(x0);
const float yend = y0 + gradient * (xend - x0);
const float xgap = rfpart(x0 + 0.5);
xpx11 = int(xend);
const int ypx11 = ipart(yend);
if (steep) {
plot(ypx11, xpx11, rfpart(yend) * xgap);
plot(ypx11 + 1, xpx11, fpart(yend) * xgap);
} else {
plot(xpx11, ypx11, rfpart(yend) * xgap);
plot(xpx11, ypx11 + 1, fpart(yend) * xgap);
}
intery = yend + gradient;
}
int xpx12;
{
const float xend = round(x1);
const float yend = y1 + gradient * (xend - x1);
const float xgap = rfpart(x1 + 0.5);
xpx12 = int(xend);
const int ypx12 = ipart(yend);
if (steep) {
plot(ypx12, xpx12, rfpart(yend) * xgap);
plot(ypx12 + 1, xpx12, fpart(yend) * xgap);
} else {
plot(xpx12, ypx12, rfpart(yend) * xgap);
plot(xpx12, ypx12 + 1, fpart(yend) * xgap);
}
}
if (steep) {
for (int x = xpx11 + 1; x < xpx12; x++) {
plot(ipart(intery), x, rfpart(intery));
plot(ipart(intery) + 1, x, fpart(intery));
intery += gradient;
}
} else {
for (int x = xpx11 + 1; x < xpx12; x++) {
plot(x, ipart(intery), rfpart(intery));
plot(x, ipart(intery) + 1, fpart(intery));
intery += gradient;
}
}
} </lang>
C#
<lang c> public class Line
{
private double x0, y0, x1, y1;
private Color foreColor;
private byte lineStyleMask;
private int thickness;
private float globalm;
public Line(double x0, double y0, double x1, double y1, Color color, byte lineStyleMask, int thickness)
{
this.x0 = x0;
this.y0 = y0;
this.y1 = y1;
this.x1 = x1;
this.foreColor = color;
this.lineStyleMask = lineStyleMask;
this.thickness = thickness;
}
private void plot(Bitmap bitmap, double x, double y, double c)
{
int alpha = (int)(c * 255);
if (alpha > 255) alpha = 255;
if (alpha < 0) alpha = 0;
Color color = Color.FromArgb(alpha, foreColor);
if (BitmapDrawHelper.checkIfInside((int)x, (int)y, bitmap))
{
bitmap.SetPixel((int)x, (int)y, color);
}
}
int ipart(double x) { return (int)x;}
int round(double x) {return ipart(x+0.5);}
double fpart(double x) {
if(x<0) return (1-(x-Math.Floor(x)));
return (x-Math.Floor(x));
}
double rfpart(double x) {
return 1-fpart(x);
}
public void draw(Bitmap bitmap) {
bool steep = Math.Abs(y1-y0)>Math.Abs(x1-x0);
double temp;
if(steep){
temp=x0; x0=y0; y0=temp;
temp=x1;x1=y1;y1=temp;
}
if(x0>x1){
temp = x0;x0=x1;x1=temp;
temp = y0;y0=y1;y1=temp;
}
double dx = x1-x0;
double dy = y1-y0;
double gradient = dy/dx;
double xEnd = round(x0);
double yEnd = y0+gradient*(xEnd-x0);
double xGap = rfpart(x0+0.5);
double xPixel1 = xEnd;
double yPixel1 = ipart(yEnd);
if(steep){
plot(bitmap, yPixel1, xPixel1, rfpart(yEnd)*xGap);
plot(bitmap, yPixel1+1, xPixel1, fpart(yEnd)*xGap);
}else{
plot(bitmap, xPixel1,yPixel1, rfpart(yEnd)*xGap);
plot(bitmap, xPixel1, yPixel1+1, fpart(yEnd)*xGap);
}
double intery = yEnd+gradient;
xEnd = round(x1);
yEnd = y1+gradient*(xEnd-x1);
xGap = fpart(x1+0.5);
double xPixel2 = xEnd;
double yPixel2 = ipart(yEnd);
if(steep){
plot(bitmap, yPixel2, xPixel2, rfpart(yEnd)*xGap);
plot(bitmap, yPixel2+1, xPixel2, fpart(yEnd)*xGap);
}else{
plot(bitmap, xPixel2, yPixel2, rfpart(yEnd)*xGap);
plot(bitmap, xPixel2, yPixel2+1, fpart(yEnd)*xGap);
}
if(steep){
for(int x=(int)(xPixel1+1);x<=xPixel2-1;x++){
plot(bitmap, ipart(intery), x, rfpart(intery));
plot(bitmap, ipart(intery)+1, x, fpart(intery));
intery+=gradient;
}
}else{
for(int x=(int)(xPixel1+1);x<=xPixel2-1;x++){
plot(bitmap, x,ipart(intery), rfpart(intery));
plot(bitmap, x, ipart(intery)+1, fpart(intery));
intery+=gradient;
}
}
}
}
</lang>
D
This performs the mixing of the colors, both in grey scale and RGB. <lang d>import std.math, std.algorithm, grayscale_image;
/// Plots anti-aliased line by Xiaolin Wu's line algorithm. void aaLine(Color)(ref Image!Color img,
double x1, double y1,
double x2, double y2,
in Color color) pure nothrow @safe @nogc {
// Straight translation of Wikipedia pseudocode.
// std.math.round is not pure. **
static double round(in double x) pure nothrow @safe @nogc {
return floor(x + 0.5);
}
static double fpart(in double x) pure nothrow @safe @nogc {
return x - x.floor;
}
static double rfpart(in double x) pure nothrow @safe @nogc {
return 1 - fpart(x);
}
auto dx = x2 - x1; auto dy = y2 - y1; immutable ax = dx.abs; immutable ay = dy.abs;
static Color mixColors(in Color c1, in Color c2, in double p)
pure nothrow @safe @nogc {
static if (is(Color == RGB))
return Color(cast(ubyte)(c1.r * p + c2.r * (1 - p)),
cast(ubyte)(c1.g * p + c2.g * (1 - p)),
cast(ubyte)(c1.b * p + c2.b * (1 - p)));
else
// This doesn't work for every kind of Color.
return Color(cast(ubyte)(c1 * p + c2 * (1 - p)));
}
// Plot function set here to handle the two cases of slope. void function(ref Image!Color, in int, in int, in double, in Color) pure nothrow @safe @nogc plot;
if (ax < ay) {
swap(x1, y1);
swap(x2, y2);
swap(dx, dy);
//plot = (img, x, y, p, col) {
plot = (ref img, x, y, p, col) {
assert(p >= 0.0 && p <= 1.0);
img[y, x] = mixColors(col, img[y, x], p);
};
} else {
//plot = (img, x, y, p, col) {
plot = (ref img, x, y, p, col) {
assert(p >= 0.0 && p <= 1.0);
img[x, y] = mixColors(col, img[x, y], p);
};
}
if (x2 < x1) {
swap(x1, x2);
swap(y1, y2);
}
immutable gradient = dy / dx;
// Handle first endpoint. auto xEnd = round(x1); auto yEnd = y1 + gradient * (xEnd - x1); auto xGap = rfpart(x1 + 0.5); // This will be used in the main loop. immutable xpxl1 = cast(int)xEnd; immutable ypxl1 = cast(int)yEnd.floor; plot(img, xpxl1, ypxl1, rfpart(yEnd) * xGap, color); plot(img, xpxl1, ypxl1 + 1, fpart(yEnd) * xGap, color); // First y-intersection for the main loop. auto yInter = yEnd + gradient;
// Handle second endpoint. xEnd = round(x2); yEnd = y2 + gradient * (xEnd - x2); xGap = fpart(x2 + 0.5); // This will be used in the main loop. immutable xpxl2 = cast(int)xEnd; immutable ypxl2 = cast(int)yEnd.floor; plot(img, xpxl2, ypxl2, rfpart(yEnd) * xGap, color); plot(img, xpxl2, ypxl2 + 1, fpart(yEnd) * xGap, color);
// Main loop.
foreach (immutable x; xpxl1 + 1 .. xpxl2) {
plot(img, x, cast(int)yInter.floor, rfpart(yInter), color);
plot(img, x, cast(int)yInter.floor + 1, fpart(yInter), color);
yInter += gradient;
}
}
void main() {
auto im1 = new Image!Gray(400, 300);
im1.clear(Gray.white);
im1.aaLine(7.4, 12.3, 307, 122.5, Gray.black);
im1.aaLine(177.4, 12.3, 127, 222.5, Gray.black);
im1.savePGM("xiaolin_lines1.pgm");
auto im2 = new Image!RGB(400, 300);
im2.clear(RGB(0, 255, 0));
immutable red = RGB(255, 0, 0);
im2.aaLine(7.4, 12.3, 307, 122.5, red);
im2.aaLine(177.4, 12.3, 127, 222.5, red);
im2.savePPM6("xiaolin_lines2.ppm");
}</lang>
FreeBASIC
This implementation follows the pseudocode given on Wikipedia. Only changed xend=round() in xend=ipart() to make it more in line with FreeBASIC's own line drawing routine. Rfpart give me some trouble so I changed if somewhat. The small functions where all converted into macro's <lang FreeBASIC>' version 21-06-2015 ' compile with: fbc -s console or fbc -s gui ' Xiaolin Wu’s line-drawing algorithm 'shared var and macro's
Dim Shared As UInteger wu_color
- Macro ipart(x)
Int(x) ' integer part
- EndMacro
- Macro round(x)
Int((x) + .5) ' round off
- EndMacro
- Macro fpart(x)
Frac(x) ' fractional part
- EndMacro
- Macro rfpart(x)
' 1 - Frac(x) ' seems to give problems for very small x IIf(1 - Frac(x) >= 1, 1, 1 - Frac(x))
- EndMacro
- Macro plot(x, y , c)
' use the alpha channel to set the amount of color PSet(x,y), wu_color Or (Int(c * 255)) Shl 24
- EndMacro
Sub drawline(x0 As Single, y0 As Single, x1 As Single, y1 As Single,_
col As UInteger = RGB(255,255,255))
wu_color = col And &HFFFFFF ' strip off the alpha channel information
Dim As Single gradient Dim As Single xend, yend, xgap, intery Dim As UInteger xpxl1, ypxl1, xpxl2, ypxl2, x Dim As Integer steep = Abs(y1 - y0) > Abs(x1 - x0) ' boolean
If steep Then
Swap x0, y0
Swap x1, y1
End If
If x0 > x1 Then
Swap x0, x1
Swap y0, y1
End If
gradient = (y1 - y0) / (x1 - x0)
' first endpoint
' xend = round(x0)
xend = ipart(x0)
yend = y0 + gradient * (xend - x0)
xgap = rfpart(x0 + .5)
xpxl1 = xend ' this will be used in the main loop
ypxl1 = ipart(yend)
If steep Then
plot(ypxl1, xpxl1, rfpart(yend) * xgap)
plot(ypxl1+1, xpxl1, fpart(yend) * xgap)
Else
plot(xpxl1, ypxl1, rfpart(yend) * xgap)
plot(xpxl1, ypxl1+1, fpart(yend) * xgap)
End If
intery = yend + gradient ' first y-intersecction for the main loop
' handle second endpoint
' xend = round(x1)
xend = ipart(x1)
yend = y1 + gradient * (xend - x1)
xgap = fpart(x1 + .5)
xpxl2 = xend ' this will be used in the main loop
ypxl2 = ipart(yend)
If steep Then
plot(ypxl2, xpxl2, rfpart(yend) * xgap)
plot(ypxl2+1, xpxl2, fpart(yend) * xgap)
Else
plot(xpxl2, ypxl2, rfpart(yend) * xgap)
plot(xpxl2, ypxl2+1, fpart(yend) * xgap)
End If
' main loop
If steep Then
For x = xpxl1 + 1 To xpxl2 - 1
plot(ipart(intery), x, rfpart(intery))
plot(ipart(intery)+1, x, fpart(intery))
intery = intery + gradient
Next
Else
For x = xpxl1 + 1 To xpxl2 - 1
plot(x, ipart(intery), rfpart(intery))
plot(x, ipart(intery)+1, fpart(intery))
intery = intery + gradient
Next
End If
End Sub
' ------=< MAIN >=------
- Define W_ 600
- Define H_ 600
- Include Once "fbgfx.bi" ' needed setting the screen attributes
Dim As Integer i Dim As String fname = __FILE__
ScreenRes W_, H_, 32,, FB.GFX_ALPHA_PRIMITIVES
Randomize Timer
For i = 0 To H_ Step H_\30
drawline(0, 0, W_, i, Int(Rnd * &HFFFFFF))
Next
For i = 0 To W_ Step W_\30
drawline(0, 0, i, H_, Int(Rnd * &HFFFFFF))
Next
i = InStr(fname,".bas") fname = Left(fname, Len(fname)-i+1) WindowTitle fname + " hit any key to end program"
While Inkey <> "" : Wend Sleep End</lang>
Go
<lang go>package raster
import "math"
func ipart(x float64) float64 {
return math.Floor(x)
}
func round(x float64) float64 {
return ipart(x + .5)
}
func fpart(x float64) float64 {
return x - ipart(x)
}
func rfpart(x float64) float64 {
return 1 - fpart(x)
}
// AaLine plots anti-aliased line by Xiaolin Wu's line algorithm. func (g *Grmap) AaLine(x1, y1, x2, y2 float64) {
// straight translation of WP pseudocode
dx := x2 - x1
dy := y2 - y1
ax := dx
if ax < 0 {
ax = -ax
}
ay := dy
if ay < 0 {
ay = -ay
}
// plot function set here to handle the two cases of slope
var plot func(int, int, float64)
if ax < ay {
x1, y1 = y1, x1
x2, y2 = y2, x2
dx, dy = dy, dx
plot = func(x, y int, c float64) {
g.SetPx(y, x, uint16(c*math.MaxUint16))
}
} else {
plot = func(x, y int, c float64) {
g.SetPx(x, y, uint16(c*math.MaxUint16))
}
}
if x2 < x1 {
x1, x2 = x2, x1
y1, y2 = y2, y1
}
gradient := dy / dx
// handle first endpoint xend := round(x1) yend := y1 + gradient*(xend-x1) xgap := rfpart(x1 + .5) xpxl1 := int(xend) // this will be used in the main loop ypxl1 := int(ipart(yend)) plot(xpxl1, ypxl1, rfpart(yend)*xgap) plot(xpxl1, ypxl1+1, fpart(yend)*xgap) intery := yend + gradient // first y-intersection for the main loop
// handle second endpoint xend = round(x2) yend = y2 + gradient*(xend-x2) xgap = fpart(x2 + 0.5) xpxl2 := int(xend) // this will be used in the main loop ypxl2 := int(ipart(yend)) plot(xpxl2, ypxl2, rfpart(yend)*xgap) plot(xpxl2, ypxl2+1, fpart(yend)*xgap)
// main loop
for x := xpxl1 + 1; x <= xpxl2-1; x++ {
plot(x, int(ipart(intery)), rfpart(intery))
plot(x, int(ipart(intery))+1, fpart(intery))
intery = intery + gradient
}
}</lang> Demonstration program: <lang go>package main
// Files required to build supporting package raster are found in: // * This task (immediately above) // * Bitmap // * Grayscale image // * Write a PPM file
import "raster"
func main() {
g := raster.NewGrmap(400, 300)
g.AaLine(7.4, 12.3, 307, 122.5)
g.AaLine(177.4, 12.3, 127, 222.5)
g.Bitmap().WritePpmFile("wu.ppm")
}</lang>
Haskell
Example makes use of JuicyPixels for serialization to PNG format and and primitive to abstract away memory-related operations. This is a fairly close translation of the algorithm as described on Wikipedia:
<lang haskell>{-# LANGUAGE ScopedTypeVariables #-}
module Main (main) where
import Codec.Picture (writePng) import Codec.Picture.Types (Image, MutableImage(..), Pixel, PixelRGB8(..), createMutableImage, unsafeFreezeImage, writePixel) import Control.Monad (void) import Control.Monad.Primitive (PrimMonad, PrimState) import Data.Foldable (foldlM)
type MImage m px = MutableImage (PrimState m) px
-- | Create an image given a function to apply to an empty mutable image withMutableImage
:: (Pixel px, PrimMonad m) => Int -- ^ image width -> Int -- ^ image height -> px -- ^ background colour -> (MImage m px -> m ()) -- ^ function to apply to mutable image -> m (Image px) -- ^ action
withMutableImage w h px f = createMutableImage w h px >>= \m -> f m >> unsafeFreezeImage m
-- | Plot a pixel at the given point in the given colour plot
:: (Pixel px, PrimMonad m) => MImage m px -- ^ mutable image -> Int -- ^ x-coordinate of point -> Int -- ^ y-coordinate of point -> px -- ^ colour -> m () -- ^ action
plot = writePixel
-- | Draw an antialiased line from first point to second point in given colour drawAntialiasedLine
:: forall px m . (Pixel px, PrimMonad m) => MImage m px -- ^ mutable image -> Int -- ^ x-coordinate of first point -> Int -- ^ y-coordinate of first point -> Int -- ^ x-coordinate of second point -> Int -- ^ y-coordinate of second point -> (Double -> px) -- ^ colour generator function -> m () -- ^ action
drawAntialiasedLine m p1x p1y p2x p2y colour = do
let steep = abs (p2y - p1y) > abs (p2x - p1x)
((p3x, p4x), (p3y, p4y)) = swapIf steep ((p1x, p2x), (p1y, p2y))
((ax, ay), (bx, by)) = swapIf (p3x > p4x) ((p3x, p3y), (p4x, p4y))
dx = bx - ax
dy = by - ay
gradient = if dx == 0 then 1.0 else fromIntegral dy / fromIntegral dx
-- handle first endpoint
let xpxl1 = ax -- round (fromIntegral ax)
yend1 = fromIntegral ay + gradient * fromIntegral (xpxl1 - ax)
xgap1 = rfpart (fromIntegral ax + 0.5)
endpoint steep xpxl1 yend1 xgap1
-- handle second endpoint
let xpxl2 = bx -- round (fromIntegral bx)
yend2 = fromIntegral by + gradient * fromIntegral (xpxl2 - bx)
xgap2 = fpart (fromIntegral bx + 0.5)
endpoint steep xpxl2 yend2 xgap2
-- main loop
let intery = yend1 + gradient
void $ if steep
then foldlM (\i x -> do
plot m (ipart i) x (colour (rfpart i))
plot m (ipart i + 1) x (colour (fpart i))
pure $ i + gradient) intery [xpxl1 + 1..xpxl2 - 1]
else foldlM (\i x -> do
plot m x (ipart i) (colour (rfpart i))
plot m x (ipart i + 1) (colour (fpart i))
pure $ i + gradient) intery [xpxl1 + 1..xpxl2 - 1]
where
endpoint :: Bool -> Int -> Double -> Double -> m ()
endpoint True xpxl yend xgap = do
plot m ypxl xpxl (colour (rfpart yend * xgap))
plot m (ypxl + 1) xpxl (colour (fpart yend * xgap))
where ypxl = ipart yend
endpoint False xpxl yend xgap = do
plot m xpxl ypxl (colour (rfpart yend * xgap))
plot m xpxl (ypxl + 1) (colour (fpart yend * xgap))
where ypxl = ipart yend
swapIf :: Bool -> (a, a) -> (a, a) swapIf False p = p swapIf True (x, y) = (y, x)
ipart :: Double -> Int ipart = truncate
fpart :: Double -> Double fpart x
| x > 0 = x - temp | otherwise = x - (temp + 1) where temp = fromIntegral (ipart x)
rfpart :: Double -> Double rfpart x = 1 - fpart x
main :: IO () main = do
-- We start and end the line with sufficient clearance from the edge of the
-- image to be able to see the endpoints
img <- withMutableImage 640 480 (PixelRGB8 0 0 0) $ \m@(MutableImage w h _) ->
drawAntialiasedLine m 2 2 (w - 2) (h - 2)
(\brightness -> let level = round (brightness * 255) in PixelRGB8 level level level)
-- Write it out to a file on disc writePng "xiaolin-wu-algorithm.png" img</lang>
Building and running this program will generate an output PNG file named xiaolin-wu-algorithm.png showing a white antialiased diagonal line.
J
Solution: <lang j>load'gl2' coinsert'jgl2'
drawpt=:4 :0"0 1
glrgb <.(-.x)*255 255 255 glpixel y
)
drawLine=:3 :0 NB. drawline x1,y1,x2,y2
pts=. 2 2$y isreversed=. </ |d=. -~/pts r=. |.^:isreversed"1 pts=. /:~ pts \:"1 |d gradient=. %~/ (\:|)d
'x y'=. |:pts xend=. <.0.5+ x yend=. y + gradient* xend-x xgap=. -.1|x+0.5
n=. i. >: -~/ xend
'xlist ylist'=. (n*/~1,gradient) + ({.xend),({.yend)
weights=. ((2&}.,~ xgap*2&{.)&.(_1&|.) (,.~-.) 1|ylist)
weights (drawpt r)"1 2 (,:+&0 1)"1 xlist,.<.ylist
)</lang>
Example use: <lang j> wd'pc win closeok; xywh 0 0 300 200;cc g isigraph; pas 0 0; pshow;' NB. J6 or earlier
wd'pc win closeok; minwh 600 400;cc g isidraw flush; pshow;' NB. J802 or later glpaint glclear glpaint drawLine 10 10 590 390</lang>
Java
<lang java>import java.awt.*; import static java.lang.Math.*; import javax.swing.*;
public class XiaolinWu extends JPanel {
public XiaolinWu() {
Dimension dim = new Dimension(640, 640);
setPreferredSize(dim);
setBackground(Color.white);
}
void plot(Graphics2D g, double x, double y, double c) {
g.setColor(new Color(0f, 0f, 0f, (float)c));
g.fillOval((int) x, (int) y, 2, 2);
}
int ipart(double x) {
return (int) x;
}
double fpart(double x) {
return x - floor(x);
}
double rfpart(double x) {
return 1.0 - fpart(x);
}
void drawLine(Graphics2D g, double x0, double y0, double x1, double y1) {
boolean steep = abs(y1 - y0) > abs(x1 - x0);
if (steep)
drawLine(g, y0, x0, y1, x1);
if (x0 > x1)
drawLine(g, x1, y1, x0, y0);
double dx = x1 - x0;
double dy = y1 - y0;
double gradient = dy / dx;
// handle first endpoint
double xend = round(x0);
double yend = y0 + gradient * (xend - x0);
double xgap = rfpart(x0 + 0.5);
double xpxl1 = xend; // this will be used in the main loop
double ypxl1 = ipart(yend);
if (steep) {
plot(g, ypxl1, xpxl1, rfpart(yend) * xgap);
plot(g, ypxl1 + 1, xpxl1, fpart(yend) * xgap);
} else {
plot(g, xpxl1, ypxl1, rfpart(yend) * xgap);
plot(g, xpxl1, ypxl1 + 1, fpart(yend) * xgap);
}
// first y-intersection for the main loop
double intery = yend + gradient;
// handle second endpoint
xend = round(x1);
yend = y1 + gradient * (xend - x1);
xgap = fpart(x1 + 0.5);
double xpxl2 = xend; // this will be used in the main loop
double ypxl2 = ipart(yend);
if (steep) {
plot(g, ypxl2, xpxl2, rfpart(yend) * xgap);
plot(g, ypxl2 + 1, xpxl2, fpart(yend) * xgap);
} else {
plot(g, xpxl2, ypxl2, rfpart(yend) * xgap);
plot(g, xpxl2, ypxl2 + 1, fpart(yend) * xgap);
}
// main loop
for (double x = xpxl1 + 1; x <= xpxl2 - 1; x++) {
if (steep) {
plot(g, ipart(intery), x, rfpart(intery));
plot(g, ipart(intery) + 1, x, fpart(intery));
} else {
plot(g, x, ipart(intery), rfpart(intery));
plot(g, x, ipart(intery) + 1, fpart(intery));
}
intery = intery + gradient;
}
}
@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
drawLine(g, 550, 170, 50, 435); }
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Xiaolin Wu's line algorithm");
f.setResizable(false);
f.add(new XiaolinWu(), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}</lang>
Julia
<lang julia>using Images
fpart(x) = mod(x, one(x)) rfpart(x) = one(x) - fpart(x)
function drawline!(img::Matrix{Gray{N0f8}}, x0::Integer, y0::Integer, x1::Integer, y1::Integer)
steep = abs(y1 - y0) > abs(x1 - x0)
if steep
x0, y0 = y0, x0
x1, y1 = y1, x1
end
if x0 > x1
x0, x1 = x1, x0
y0, y1 = y1, y0
end
dx = x1 - x0 dy = y1 - y0 grad = dy / dx
if iszero(dx)
grad = oftype(grad, 1.0)
end
# handle first endpoint xend = round(Int, x0) yend = y0 + grad * (xend - x0) xgap = rfpart(x0 + 0.5) xpxl1 = xend ypxl1 = floor(Int, yend)
if steep
img[ypxl1, xpxl1] = rfpart(yend) * xgap
img[ypxl1+1, xpxl1] = fpart(yend) * xgap
else
img[xpxl1, ypxl1 ] = rfpart(yend) * xgap
img[xpxl1, ypxl1+1] = fpart(yend) * xgap
end
intery = yend + grad # first y-intersection for the main loop
# handle second endpoint
xend = round(Int, x1)
yend = y1 + grad * (xend - x1)
xgap = fpart(x1 + 0.5)
xpxl2 = xend
ypxl2 = floor(Int, yend)
if steep
img[ypxl2, xpxl2] = rfpart(yend) * xgap
img[ypxl2+1, xpxl2] = fpart(yend) * xgap
else
img[xpxl2, ypxl2 ] = rfpart(yend) * xgap
img[xpxl2, ypxl2+1] = fpart(yend) * xgap
end
# main loop
if steep
for x in xpxl1+1:xpxl2-1
img[floor(Int, intery), x] = rfpart(intery)
img[floor(Int, intery)+1, x] = fpart(intery)
intery += grad
end
else
for x in xpxl1+1:xpxl2-1
img[x, floor(Int, intery) ] = rfpart(intery)
img[x, floor(Int, intery)+1] = fpart(intery)
intery += grad
end
end
return img
end
img = fill(Gray(1.0N0f8), 250, 250); drawline!(img, 8, 8, 192, 154)</lang>
Kotlin
<lang scala>// version 1.1.2
import java.awt.* import javax.swing.*
class XiaolinWu: JPanel() {
init {
preferredSize = Dimension(640, 640)
background = Color.white
}
private fun plot(g: Graphics2D, x: Double, y: Double, c: Double) {
g.color = Color(0f, 0f, 0f, c.toFloat())
g.fillOval(x.toInt(), y.toInt(), 2, 2)
}
private fun ipart(x: Double) = x.toInt()
private fun fpart(x: Double) = x - Math.floor(x)
private fun rfpart(x: Double) = 1.0 - fpart(x)
private fun drawLine(g: Graphics2D, x0: Double, y0: Double, x1: Double, y1: Double) {
val steep = Math.abs(y1 - y0) > Math.abs(x1 - x0)
if (steep) drawLine(g, y0, x0, y1, x1)
if (x0 > x1) drawLine(g, x1, y1, x0, y0)
val dx = x1 - x0
val dy = y1 - y0
val gradient = dy / dx
// handle first endpoint
var xend = Math.round(x0).toDouble()
var yend = y0 + gradient * (xend - x0)
var xgap = rfpart(x0 + 0.5)
val xpxl1 = xend // this will be used in the main loop
val ypxl1 = ipart(yend).toDouble()
if (steep) {
plot(g, ypxl1, xpxl1, rfpart(yend) * xgap)
plot(g, ypxl1 + 1.0, xpxl1, fpart(yend) * xgap)
}
else {
plot(g, xpxl1, ypxl1, rfpart(yend) * xgap)
plot(g, xpxl1, ypxl1 + 1.0, fpart(yend) * xgap)
}
// first y-intersection for the main loop
var intery = yend + gradient
// handle second endpoint
xend = Math.round(x1).toDouble()
yend = y1 + gradient * (xend - x1)
xgap = fpart(x1 + 0.5)
val xpxl2 = xend // this will be used in the main loop
val ypxl2 = ipart(yend).toDouble()
if (steep) {
plot(g, ypxl2, xpxl2, rfpart(yend) * xgap)
plot(g, ypxl2 + 1.0, xpxl2, fpart(yend) * xgap)
}
else {
plot(g, xpxl2, ypxl2, rfpart(yend) * xgap)
plot(g, xpxl2, ypxl2 + 1.0, fpart(yend) * xgap)
}
// main loop
var x = xpxl1 + 1.0
while (x <= xpxl2 - 1) {
if (steep) {
plot(g, ipart(intery).toDouble(), x, rfpart(intery))
plot(g, ipart(intery).toDouble() + 1.0, x, fpart(intery))
}
else {
plot(g, x, ipart(intery).toDouble(), rfpart(intery))
plot(g, x, ipart(intery).toDouble() + 1.0, fpart(intery))
}
intery += gradient
x++
}
}
override protected fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
drawLine(g, 550.0, 170.0, 50.0, 435.0)
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
f.title = "Xiaolin Wu's line algorithm"
f.isResizable = false
f.add(XiaolinWu(), BorderLayout.CENTER)
f.pack()
f.setLocationRelativeTo(null)
f.isVisible = true
}
}</lang>
Liberty BASIC
<lang lb> NoMainWin WindowWidth = 270 WindowHeight = 290 UpperLeftX=int((DisplayWidth-WindowWidth)/2) UpperLeftY=int((DisplayHeight-WindowHeight)/2)
Global variablesInitialized : variablesInitialized = 0 Global BackColor$ : BackColor$ = "0 0 0" ' BackColor$ = "255 255 255"
'now, right click randomizes BG
Global size : size = 1'4 global mousepoints.mouseX0, mousepoints.mouseY0, mousepoints.mouseX1, mousepoints.mouseY1
'StyleBits #main.gbox, 0, _WS_BORDER, 0, 0 GraphicBox #main.gbox, 0, 0, 253, 252
Open "Click Twice to Form Line" For Window As #main Print #main, "TrapClose quit" Print #main.gbox, "Down; Color Black" Print #main.gbox, "Down; fill ";BackColor$ Print #main.gbox, "When leftButtonUp gBoxClick" Print #main.gbox, "When rightButtonUp RandomBG" Print #main.gbox, "Size "; size
result = drawAntiAliasedLine(126.5, 0, 126.5, 252, "255 0 0") result = drawAntiAliasedLine(0, 126, 253, 126, "255 0 0") result = drawAntiAliasedLine(0, 0, 253, 252, "255 0 0") result = drawAntiAliasedLine(253, 0, 0, 252, "255 0 0") Wait
Sub quit handle$
Close #main
End
End Sub
sub RandomBG handle$, MouseX, MouseY
BackColor$ = int(rnd(1)*256);" ";int(rnd(1)*256);" ";int(rnd(1)*256) Print #main.gbox, "CLS; fill ";BackColor$ variablesInitialized = 0
end sub
Sub gBoxClick handle$, MouseX, MouseY
'We will use the mousepoints "struct" to hold the values
'that way they are retained between subroutine calls
If variablesInitialized = 0 Then
Print #main.gbox, "CLS; fill ";BackColor$
mousepoints.mouseX0 = MouseX
mousepoints.mouseY0 = MouseY
variablesInitialized = 1
Else
If variablesInitialized = 1 Then
mousepoints.mouseX1 = MouseX
mousepoints.mouseY1 = MouseY
variablesInitialized = 0
result = drawAntiAliasedLine(mousepoints.mouseX0, mousepoints.mouseY0, mousepoints.mouseX1, mousepoints.mouseY1, "255 0 0")
End If
End If
End Sub
Function Swap(Byref a,Byref b)
aTemp = b
b = a
a = aTemp
End Function
Function RoundtoInt(val)
RoundtoInt = Int(val + 0.5)
End Function
Function PlotAntiAliased(x, y, RGB$, b, steep)
RGB$ = Int(Val(Word$(BackColor$, 1))*(1-b) + Val(Word$(RGB$, 1)) * b) ; " " ; _
Int(Val(Word$(BackColor$, 2))*(1-b) + Val(Word$(RGB$, 3)) * b) ; " " ; _
Int(Val(Word$(BackColor$, 3))*(1-b) + Val(Word$(RGB$, 2)) * b)
if steep then 'x and y reversed
Print #main.gbox, "Down; Color " + RGB$ + "; Set " + str$(y) + " " + str$(x)
else
Print #main.gbox, "Down; Color " + RGB$ + "; Set " + str$(x) + " " + str$(y)
end if
End Function
Function fracPart(x)
fracPart = (x Mod 1)
End function
Function invFracPart(x)
invFracPart = (1 - fracPart(x))
End Function
Function drawAntiAliasedLine(x1, y1, x2, y2, RGB$)
If (x2 - x1)=0 Or (y2 - y1)=0 Then
Print #main.gbox, "Down; Color " + RGB$
result = BresenhamLine(x1, y1, x2, y2)
Exit Function
End If
steep = abs(x2 - x1) < abs(y2 - y1)
if steep then 'x and y should be reversed
result = Swap(x1, y1)
result = Swap(x2, y2)
end if
If (x2 < x1) Then
result = Swap(x1, x2)
result = Swap(y1, y2)
End If
dx = (x2 - x1)
dy = (y2 - y1)
grad = (dy/ dx)
'Handle the First EndPoint
xend = RoundtoInt(x1)
yend = y1 + grad * (xend - x1)
xgap = invFracPart(x1 + 0.5)
ix1 = xend
iy1 = Int(yend)
result = PlotAntiAliased(ix1, iy1, RGB$, invFracPart(yend) * xgap, steep )
result = PlotAntiAliased(ix1, (iy1 + size), RGB$, fracPart(yend) * xgap, steep )
yf = (yend + grad)
'Handle the Second EndPoint
xend = RoundtoInt(x2)
yend = y2 + grad * (xend - x2)
xgap = fracPart(x2 + 0.5)
ix2 = xend
iy2 = Int(yend)
result = PlotAntiAliased(ix2, iy2, RGB$, invFracPart(yend) * xgap, steep )
result = PlotAntiAliased(ix2, (iy2 + size), RGB$, fracPart(yend) * xgap, steep )
For x = ix1 + 1 To ix2 - 1
result = PlotAntiAliased(x, Int(yf), RGB$, invFracPart(yf), steep )
result = PlotAntiAliased(x, (Int(yf) + size), RGB$, fracPart(yf), steep )
yf = (yf + grad)
Next x
End Function
Function BresenhamLine(x0, y0, x1, y1)
dx = Abs(x1 - x0)
dy = Abs(y1 - y0)
sx = ((x1 > x0) + Not(x0 < x1))
sy = ((y1 > y0) + Not(y0 < y1))
errornum = (dx - dy)
Do While 1
Print #main.gbox, "Set " + str$(x0) + " " + str$(y0)
If (x0 = x1) And (y0 = y1) Then Exit Do
errornum2 = (2 * errornum)
If errornum2 > (-1 * dy) Then
errornum = (errornum - dy)
x0 = (x0 + sx)
End If
If errornum2 < dx Then
errornum = (errornum + dx)
y0 = (y0 + sy)
End If
Loop
End Function
</lang>
Pascal
Based on Wikipwdia pseudocode with some optimizations and alpha handling.
<lang pascal> program wu; uses
SDL2, math;
const
FPS = 1000 div 60; SCALE = 6;
var
win: PSDL_Window; ren: PSDL_Renderer; mouse_x, mouse_y: longint; origin: TSDL_Point; event: TSDL_Event; line_alpha: byte = 255;
procedure SDL_RenderDrawWuLine(renderer: PSDL_Renderer; x1, y1, x2, y2: longint); var
r, g, b, a, a_new: Uint8; gradient, iy: real; x, y: longint; px, py: plongint;
procedure swap(var a, b: longint); var tmp: longint; begin tmp := a; a := b; b := tmp; end;
begin
if a = 0 then
exit;
SDL_GetRenderDrawColor(renderer, @r, @g, @b, @a);
if abs(y2 - y1) > abs(x2 - x1) then
begin
swap(x1, y1);
swap(x2, y2);
px := @y;
py := @x;
end
else
begin
px := @x;
py := @y;
end;
if x1 > x2 then
begin
swap(x1, x2);
swap(y1, y2);
end;
x := x2 - x1;
if x = 0 then
x := 1;
gradient := (y2 - y1) / x;
iy := y1;
for x := x1 to x2 do
begin
a_new := round(a * frac(iy));
y := floor(iy);
SDL_SetRenderDrawColor(renderer, r, g, b, a-a_new);
SDL_RenderDrawPoint(renderer, px^, py^);
inc(y);
SDL_SetRenderDrawColor(renderer, r, g, b, a_new);
SDL_RenderDrawPoint(renderer, px^, py^);
iy := iy + gradient;
end;
SDL_SetRenderDrawColor(renderer, r, g, b, a);
end;
begin
SDL_Init(SDL_INIT_VIDEO);
win := SDL_CreateWindow('Xiaolin Wus line algorithm', SDL_WINDOWPOS_CENTERED, SDL_WINDOWPOS_CENTERED,
640, 480, SDL_WINDOW_RESIZABLE);
ren := SDL_CreateRenderer(win, -1, 0);
if ren = NIL then
begin
writeln(SDL_GetError);
halt;
end;
SDL_SetRenderDrawBlendMode(ren, SDL_BLENDMODE_BLEND);
SDL_RenderSetScale(ren, SCALE, SCALE);
SDL_SetCursor(SDL_CreateSystemCursor(SDL_SYSTEM_CURSOR_CROSSHAIR));
mouse_x := 0;
mouse_y := 0;
origin.x := 0;
origin.y := 0;
repeat
while SDL_PollEvent(@event) = 1 do
case event.type_ of
SDL_KEYDOWN:
if event.key.keysym.sym = SDLK_ESCAPE then
halt;
SDL_MOUSEBUTTONDOWN:
begin
origin.x := mouse_x;
origin.y := mouse_y;
end;
SDL_MOUSEMOTION:
with event.motion do
begin
mouse_x := x div SCALE;
mouse_y := y div SCALE;
end;
SDL_MOUSEWHEEL:
line_alpha := EnsureRange(line_alpha + event.wheel.y * 20, 0, 255);
SDL_QUITEV:
halt;
end;
SDL_SetRenderDrawColor(ren, 35, 35, 35, line_alpha); SDL_RenderDrawWuLine(ren, origin.x, origin.y, mouse_x, mouse_y); SDL_RenderPresent(ren); SDL_SetRenderDrawColor(ren, 255, 255, 255, 255); SDL_RenderClear(ren); SDL_Delay(FPS); until false;
end. </lang>
Perl
This is mostly a translation of the pseudo-code on Wikipedia, except that the $plot trick was inspired by the perl6 RosettaCode example. <lang perl>#!perl use strict; use warnings;
sub plot { my ($x, $y, $c) = @_; printf "plot %d %d %.1f\n", $x, $y, $c if $c; }
sub ipart { int shift; }
sub round { int( 0.5 + shift ); }
sub fpart { my $x = shift; $x - int $x; }
sub rfpart { 1 - fpart(shift); }
sub drawLine { my ($x0, $y0, $x1, $y1) = @_;
my $plot = \&plot;
if( abs($y1 - $y0) > abs($x1 - $x0) ) { $plot = sub { plot( @_[1, 0, 2] ) }; ($x0, $y0, $x1, $y1) = ($y0, $x0, $y1, $x1); }
if( $x0 > $x1 ) { ($x0, $x1, $y0, $y1) = ($x1, $x0, $y1, $y0); }
my $dx = $x1 - $x0; my $dy = $y1 - $y0; my $gradient = $dy / $dx;
my @xends; my $intery;
# handle the endpoints for my $xy ([$x0, $y0], [$x1, $y1]) { my ($x, $y) = @$xy; my $xend = round($x); my $yend = $y + $gradient * ($xend - $x); my $xgap = rfpart($x + 0.5);
my $x_pixel = $xend; my $y_pixel = ipart($yend); push @xends, $x_pixel;
$plot->($x_pixel, $y_pixel , rfpart($yend) * $xgap); $plot->($x_pixel, $y_pixel+1, fpart($yend) * $xgap); next if defined $intery; # first y-intersection for the main loop $intery = $yend + $gradient; }
# main loop
for my $x ( $xends[0] + 1 .. $xends[1] - 1 ) { $plot->($x, ipart ($intery), rfpart($intery)); $plot->($x, ipart ($intery)+1, fpart($intery)); $intery += $gradient; } }
if( $0 eq __FILE__ ) { drawLine( 0, 1, 10, 2 ); } __END__ </lang>
- Output:
plot 0 1 0.5 plot 10 2 0.5 plot 1 1 0.9 plot 1 2 0.1 plot 2 1 0.8 plot 2 2 0.2 plot 3 1 0.7 plot 3 2 0.3 plot 4 1 0.6 plot 4 2 0.4 plot 5 1 0.5 plot 5 2 0.5 plot 6 1 0.4 plot 6 2 0.6 plot 7 1 0.3 plot 7 2 0.7 plot 8 1 0.2 plot 8 2 0.8 plot 9 1 0.1 plot 9 2 0.9
Phix
For educational/comparison purposes only: see demo\pGUI\aaline.exw for a much shorter version.
Resize the window to show lines at any angle
<lang Phix>-- -- demo\rosetta\XiaolinWuLine.exw -- ============================== -- constant TITLE = "Xiaolin Wu's line algorithm"
bool bresline = false -- space toggles, for comparison
include pGUI.e
Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas
constant BACK = CD_PARCHMENT,
LINE = CD_BLUE,
rB = red(BACK), gB = green(BACK), bB = blue(BACK),
rL = red(LINE), gL = green(LINE), bL = blue(LINE)
procedure plot(atom x, atom y, atom c, bool steep=false) -- plot the pixel at (x, y) with brightness c (where 0 <= c <= 1)
if steep then {x,y} = {y,x} end if
atom C = 1-c
c = rgb(rL*c+rB*C,gL*c+gB*C,bL*c+bB*C)
cdCanvasPixel(cddbuffer, x, y, c)
end procedure
procedure plot2(atom x, atom y, atom f, atom xgap, bool steep)
plot(x,y,(1-f)*xgap,steep) plot(x,y+1,f*xgap,steep)
end procedure
function fpart(atom x)
return x - floor(x) -- fractional part of x
end function
procedure draw_line(atom x0,y0,x1,y1)
if bresline then
cdCanvasLine(cddbuffer, x0, y0, x1, y1)
return
end if
bool steep := abs(y1 - y0) > abs(x1 - x0)
if steep then
{x0, y0, x1, y1} = {y0, x0, y1, x1}
end if
if x0>x1 then
{x0, x1, y0, y1} = {x1, x0, y1, y0}
end if
atom dx := x1 - x0,
dy := y1 - y0,
gradient := iff(dx=0? 1 : dy / dx)
-- handle first endpoint
atom xend := round(x0),
yend := y0 + gradient * (xend - x0),
xgap := 1-fpart(x0 + 0.5),
xpxl1 := xend, -- this will be used in the main loop
ypxl1 := floor(yend)
plot2(xpxl1, ypxl1, fpart(yend), xgap, steep)
atom intery := yend + gradient -- first y-intersection for the main loop
-- handle second endpoint
xend := round(x1)
yend := y1 + gradient * (xend - x1)
xgap := fpart(x1 + 0.5)
atom xpxl2 := xend, -- this will be used in the main loop
ypxl2 := floor(yend)
plot2(xpxl2, ypxl2, fpart(yend), xgap, steep)
-- main loop
for x = xpxl1+1 to xpxl2-1 do
plot2(x, floor(intery), fpart(intery), 1, steep)
intery += gradient
end for
end procedure
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
integer {w, h} = sq_sub(IupGetIntInt(canvas, "DRAWSIZE"),10)
cdCanvasActivate(cddbuffer)
cdCanvasClear(cddbuffer)
draw_line(0,0,200,200)
draw_line(w,0,200,200)
draw_line(0,h,200,200)
draw_line(w,h,200,200)
cdCanvasFlush(cddbuffer)
return IUP_DEFAULT
end function
function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih) cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas) cdCanvasSetBackground(cddbuffer, BACK) cdCanvasSetForeground(cddbuffer, LINE) return IUP_DEFAULT
end function
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
if c=' ' then
bresline = not bresline
IupRedraw(canvas)
end if
return IUP_CONTINUE
end function
procedure main()
IupOpen()
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "640x480")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", TITLE)
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupShow(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL)
IupMainLoop()
IupClose()
end procedure main()</lang>
PicoLisp
<lang PicoLisp>(scl 2)
(de plot (Img X Y C)
(set (nth Img (*/ Y 1.0) (*/ X 1.0)) (- 100 C)) )
(de ipart (X)
(* 1.0 (/ X 1.0)) )
(de iround (X)
(ipart (+ X 0.5)) )
(de fpart (X)
(% X 1.0) )
(de rfpart (X)
(- 1.0 (fpart X)) )
(de xiaolin (Img X1 Y1 X2 Y2)
(let (DX (- X2 X1) DY (- Y2 Y1))
(use (Grad Xend Yend Xgap Xpxl1 Ypxl1 Xpxl2 Ypxl2 Intery)
(when (> (abs DY) (abs DX))
(xchg 'X1 'Y1 'X2 'Y2) )
(when (> X1 X2)
(xchg 'X1 'X2 'Y1 'Y2) )
(setq
Grad (*/ DY 1.0 DX)
Xend (iround X1)
Yend (+ Y1 (*/ Grad (- Xend X1) 1.0))
Xgap (rfpart (+ X1 0.5))
Xpxl1 Xend
Ypxl1 (ipart Yend) )
(plot Img Xpxl1 Ypxl1 (*/ (rfpart Yend) Xgap 1.0))
(plot Img Xpxl1 (+ 1.0 Ypxl1) (*/ (fpart Yend) Xgap 1.0))
(setq
Intery (+ Yend Grad)
Xend (iround X2)
Yend (+ Y2 (*/ Grad (- Xend X2) 1.0))
Xgap (fpart (+ X2 0.5))
Xpxl2 Xend
Ypxl2 (ipart Yend) )
(plot Img Xpxl2 Ypxl2 (*/ (rfpart Yend) Xgap 1.0))
(plot Img Xpxl2 (+ 1.0 Ypxl2) (*/ (fpart Yend) Xgap 1.0))
(for (X (+ Xpxl1 1.0) (>= (- Xpxl2 1.0) X) (+ X 1.0))
(plot Img X (ipart Intery) (rfpart Intery))
(plot Img X (+ 1.0 (ipart Intery)) (fpart Intery))
(inc 'Intery Grad) ) ) ) )
(let Img (make (do 90 (link (need 120 99)))) # Create image 120 x 90
(xiaolin Img 10.0 10.0 110.0 80.0) # Draw lines
(xiaolin Img 10.0 10.0 110.0 45.0)
(xiaolin Img 10.0 80.0 110.0 45.0)
(xiaolin Img 10.0 80.0 110.0 10.0)
(out "img.pgm" # Write to bitmap file
(prinl "P2")
(prinl 120 " " 90)
(prinl 100)
(for Y Img (apply printsp Y)) ) )</lang>
PureBasic
<lang PureBasic>Macro PlotB(x, y, Color, b)
Plot(x, y, RGB(Red(Color) * (b), Green(Color) * (b), Blue(Color) * (b)))
EndMacro
Procedure.f fracPart(x.f)
ProcedureReturn x - Int(x)
EndProcedure
Procedure.f invFracPart(x.f)
ProcedureReturn 1.0 - fracPart(x)
EndProcedure
Procedure drawAntiAliasedLine(x1.f, y1.f, x2.f, y2.f, color)
Protected.f dx, dy, xend, yend, grad, yf, xgap, ix1, iy1, ix2, iy2 Protected x dx = x2 - x1 dy = y2 - y1 If Abs(dx) < Abs(dy) Swap x1, y1 Swap x2, y2 Swap dx, dy EndIf If x2 < x1 Swap x1, x2 Swap y1, y2 EndIf grad = dy / dx ;handle first endpoint xend = Round(x1, #pb_round_nearest) yend = y1 + grad * (xend - x1) xgap = invFracPart(x1 + 0.5) ix1 = xend ;this will be used in the MAIN loop iy1 = Int(yend) PlotB(ix1, iy1, color, invFracPart(yend) * xgap) PlotB(ix1, iy1 + 1, color, fracPart(yend) * xgap) yf = yend + grad ;first y-intersection for the MAIN loop ;handle second endpoint xend = Round(x2, #pb_round_nearest) yend = y2 + grad * (xend - x2) xgap = fracPart(x2 + 0.5) ix2 = xend ;this will be used in the MAIN loop iy2 = Int(yend) PlotB(ix2, iy2, color, invFracPart(yend) * xgap) PlotB(ix2, iy2 + 1, color, fracPart(yend) * xgap) ;MAIN loop For x = ix1 + 1 To ix2 - 1 PlotB(x, Int(yf), color, invFracPart(yf)) PlotB(x, Int(yf) + 1, color, fracPart(yf)) yf + grad Next
EndProcedure
Define w = 200, h = 200, img = 1 CreateImage(img, w, h) ;img is internal id of the image
OpenWindow(0, 0, 0, w, h,"Xiaolin Wu's line algorithm", #PB_Window_SystemMenu)
StartDrawing(ImageOutput(img))
drawAntiAliasedLine(80,20, 130,80, RGB(255, 0, 0))
StopDrawing()
ImageGadget(0, 0, 0, w, h, ImageID(img))
Define event Repeat
event = WaitWindowEvent()
Until event = #PB_Event_CloseWindow</lang>
Python
<lang python>"""Script demonstrating drawing of anti-aliased lines using Xiaolin Wu's line algorithm
usage: python xiaolinwu.py [output-file]
""" from __future__ import division import sys
from PIL import Image
def _fpart(x):
return x - int(x)
def _rfpart(x):
return 1 - _fpart(x)
def putpixel(img, xy, color, alpha=1):
"""Paints color over the background at the point xy in img. Use alpha for blending. alpha=1 means a completely opaque foreground.
"""
c = tuple(map(lambda bg, fg: int(round(alpha * fg + (1-alpha) * bg)),
img.getpixel(xy), color))
img.putpixel(xy, c)
def draw_line(img, p1, p2, color):
"""Draws an anti-aliased line in img from p1 to p2 with the given color.""" x1, y1 = p1 x2, y2 = p2 dx, dy = x2-x1, y2-y1 steep = abs(dx) < abs(dy) p = lambda px, py: ((px,py), (py,px))[steep]
if steep:
x1, y1, x2, y2, dx, dy = y1, x1, y2, x2, dy, dx
if x2 < x1:
x1, x2, y1, y2 = x2, x1, y2, y1
grad = dy/dx
intery = y1 + _rfpart(x1) * grad
def draw_endpoint(pt):
x, y = pt
xend = round(x)
yend = y + grad * (xend - x)
xgap = _rfpart(x + 0.5)
px, py = int(xend), int(yend)
putpixel(img, p(px, py), color, _rfpart(yend) * xgap)
putpixel(img, p(px, py+1), color, _fpart(yend) * xgap)
return px
xstart = draw_endpoint(p(*p1)) + 1 xend = draw_endpoint(p(*p2))
for x in range(xstart, xend):
y = int(intery)
putpixel(img, p(x, y), color, _rfpart(intery))
putpixel(img, p(x, y+1), color, _fpart(intery))
intery += grad
if __name__ == '__main__':
if len(sys.argv) != 2:
print 'usage: python xiaolinwu.py [output-file]'
sys.exit(-1)
blue = (0, 0, 255)
yellow = (255, 255, 0)
img = Image.new("RGB", (500,500), blue)
for a in range(10, 431, 60):
draw_line(img, (10, 10), (490, a), yellow)
draw_line(img, (10, 10), (a, 490), yellow)
draw_line(img, (10, 10), (490, 490), yellow)
filename = sys.argv[1]
img.save(filename)
print 'image saved to', filename</lang>
Racket
<lang racket>#lang racket (require 2htdp/image)
(define (plot img x y c)
(define c*255 (exact-round (* (- 1 c) 255))) (place-image (rectangle 1 1 'solid (make-color c*255 c*255 c*255 255)) x y img))
(define ipart exact-floor) ; assume that a "round-down" is what we want when -ve
- `round` is built in -- but we'll use exact round (and I'm not keen on over-binding round)
(define (fpart n) (- n (exact-floor n))) (define (rfpart n) (- 1 (fpart n)))
(define (draw-line img x0 y0 x1 y1)
(define (draw-line-steeped img x0 y0 x1 y1 steep?)
(define (draw-line-steeped-l-to-r img x0 y0 x1 y1 steep?)
(define dx (- x1 x0))
(define dy (- y1 y0))
(define gradient (/ dy dx))
(define (handle-end-point img x y)
(define xend (exact-round x))
(define yend (+ y (* gradient (- xend x))))
(define xgap (rfpart (+ x 0.5)))
(define ypxl (ipart yend))
(define intery (+ yend gradient))
(case steep?
[(#t)
(define img* (plot img ypxl xend (* xgap (rfpart yend))))
(values (plot img* (+ ypxl 1) xend (* xgap (fpart yend))) xend intery)]
[(#f)
(define img* (plot img xend ypxl (* xgap (rfpart yend))))
(values (plot img* xend (+ ypxl 1) (* xgap (fpart yend))) xend intery)]))
(define-values (img-with-l-endpoint xpl1 intery) (handle-end-point img x0 y0))
(define-values (img-with-r-endpoint xpl2 _) (handle-end-point img-with-l-endpoint x1 y1))
(for/fold ((img img-with-l-endpoint) (y intery))
((x (in-range (+ xpl1 1) xpl2)))
(define y-i (ipart y))
(values
(case steep?
[(#t)
(define img* (plot img y-i x (rfpart y)))
(plot img* (+ 1 y-i) x (fpart y))]
[(#f)
(define img* (plot img x y-i (rfpart y)))
(plot img* x (+ 1 y-i) (fpart y))])
(+ y gradient))))
(if (> x0 x1)
(draw-line-steeped-l-to-r img x1 y1 x0 y0 steep?)
(draw-line-steeped-l-to-r img x0 y0 x1 y1 steep?)))
(define steep? (> (abs (- y1 y0)) (abs (- x1 x0))))
(define-values (img* _)
(if steep?
(draw-line-steeped img y0 x0 y1 x1 steep?)
(draw-line-steeped img x0 y0 x1 y1 steep?)))
img*)
(define img-1 (beside
(scale 3 (draw-line (empty-scene 150 100) 12 12 138 88)) (above (scale 1 (draw-line (empty-scene 150 100) 12 50 138 50)) (scale 1 (draw-line (empty-scene 150 100) 75 12 75 88)) (scale 1 (draw-line (empty-scene 150 100) 12 88 138 12)))))
(define img-2
(beside
(scale 3 (draw-line (empty-scene 100 150) 12 12 88 138))
(above (scale 1 (draw-line (empty-scene 100 150) 50 12 50 138))
(scale 1 (draw-line (empty-scene 100 150) 12 75 88 75))
(scale 1 (draw-line (empty-scene 100 150) 88 12 12 138)))))
img-1 img-2 (save-image img-1 "images/xiaolin-wu-racket-1.png") (save-image img-2 "images/xiaolin-wu-racket-2.png")</lang>
Output files: File:Xiaolin-wu-racket-1.png File:Xiaolin-wu-racket-2.png
Raku
(formerly Perl 6) <lang perl6>sub plot(\x, \y, \c) { say "plot {x} {y} {c}" }
sub fpart(\x) { x - floor(x) }
sub draw-line(@a is copy, @b is copy) {
my Bool \steep = abs(@b[1] - @a[1]) > abs(@b[0] - @a[0]);
my $plot = &OUTER::plot;
if steep {
$plot = -> $y, $x, $c { plot($x, $y, $c) } @a.=reverse; @b.=reverse;
}
if @a[0] > @b[0] { my @t = @a; @a = @b; @b = @t }
my (\x0,\y0) = @a; my (\x1,\y1) = @b; my \dx = x1 - x0; my \dy = y1 - y0; my \gradient = dy / dx; # handle first endpoint my \x-end1 = round(x0); my \y-end1 = y0 + gradient * (x-end1 - x0); my \x-gap1 = 1 - round(x0 + 0.5);
my \x-pxl1 = x-end1; # this will be used in the main loop my \y-pxl1 = floor(y-end1); my \c1 = fpart(y-end1) * x-gap1;
$plot(x-pxl1, y-pxl1 , 1 - c1) unless c1 == 1; $plot(x-pxl1, y-pxl1 + 1, c1 ) unless c1 == 0; # handle second endpoint my \x-end2 = round(x1); my \y-end2 = y1 + gradient * (x-end2 - x1); my \x-gap2 = fpart(x1 + 0.5);
my \x-pxl2 = x-end2; # this will be used in the main loop my \y-pxl2 = floor(y-end2); my \c2 = fpart(y-end2) * x-gap2; my \intery = y-end1 + gradient;
# main loop for (x-pxl1 + 1 .. x-pxl2 - 1)
Z (intery, intery + gradient ... *)
-> (\x,\y) {
my \c = fpart(y); $plot(x, floor(y) , 1 - c) unless c == 1; $plot(x, floor(y) + 1, c ) unless c == 0;
}
$plot(x-pxl2, y-pxl2 , 1 - c2) unless c2 == 1; $plot(x-pxl2, y-pxl2 + 1, c2 ) unless c2 == 0;
}
draw-line [0,1], [10,2];</lang>
- Output:
plot 0 1 1 plot 1 1 0.9 plot 1 2 0.1 plot 2 1 0.8 plot 2 2 0.2 plot 3 1 0.7 plot 3 2 0.3 plot 4 1 0.6 plot 4 2 0.4 plot 5 1 0.5 plot 5 2 0.5 plot 6 1 0.4 plot 6 2 0.6 plot 7 1 0.3 plot 7 2 0.7 plot 8 1 0.2 plot 8 2 0.8 plot 9 1 0.1 plot 9 2 0.9 plot 10 2 1
REXX
This REXX example uses the Xiaolin Wu line algorithm to draw a line (with output).
Apparently, there may be an error in the definition of the algorithm (which only manifests itself with negative numbers):
use of the IPART function should probably be FLOOR.
[See the talk section on the Xiaolin Wu's line algorithm.]
http://en.wikipedia.org/wiki/Talk:Xiaolin_Wu%27s_line_algorithm
Also, it takes in account (that can easily be overlooked) of the note after the description of the algorithm:
Note: If at the beginning of the routine abs(dx) < abs(dy) is true, then all plotting should be done with x and y reversed.
<lang rexx>/*REXX program plots/draws (ASCII) a line using the Xiaolin Wu line algorithm. */
background= '·' /*background character: a middle-dot. */
image.= background /*fill the array with middle-dots. */
plotC= '░▒▓█' /*characters used for plotting points. */
EoE= 3000 /*EOE = End Of Earth, er, ··· graph. */
do j=-EoE to +EoE /*define the graph: lowest ──► highest.*/
image.j.0= '─' /*define the graph's horizontal axis. */
image.0.j= '│' /* " " " verical " */
end /*j*/
image.0.0= '┼' /*define the graph's axis origin (char)*/
parse arg xi yi xf yf . /*allow specifying the line-end points.*/ if xi== | xi=="," then xi= 1 /*Not specified? Then use the default.*/ if yi== | yi=="," then yi= 2 /* " " " " " " */ if xf== | xf=="," then xf=11 /* " " " " " " */ if yf== | yf=="," then yf=12 /* " " " " " " */ minX=0; minY=0 /*use these as the limits for plotting.*/ maxX=0; maxY=0 /* " " " " " " " */ call drawLine xi, yi, xf, yf /*invoke subroutine and graph the line.*/ border=2 /*allow additional space (plot border).*/ minX=minX - border * 2; maxX=maxX + border * 2 /*preserve screen's aspect ratio {*2}.*/ minY=minY - border ; maxY=maxY + border
do y=maxY to minY by -1; $= /*construct a row.*/
do x=minX to maxX; $=$ || image.x.y; end /*x*/
say $ /*display the constructed row to term. */
end /*y*/ /*graph is cropped by the MINs and MAXs*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ drawLine: parse arg x1,y1,x2,y2; switchXY=0; dx=x2-x1
dy=y2-y1
if abs(dx)<abs(dy) then parse value x1 y1 x2 y2 dx dy with y1 x2 y2 x2 dy dx
if x2<x1 then parse value x1 x2 y1 y2 1 with x2 x1 y2 y1 switchXY
gradient=dy/dx
xend=round(x1) /*◄─────────────────1st endpoint.══════════════*/
yend=y1 + gradient * (xend-x1); xgap=1 - fpart(x1 + .5)
xpx11=xend; ypx11=floor(yend)
intery=yend+gradient
call plotXY xpx11, ypx11, brite(1 - fpart(yend*xgap)), switchXY
call plotXY xpx11, ypx11+1, brite( fpart(yend*xgap)), switchXY
xend=round(x2) /*◄─────────────────2nd endpoint.══════════════*/
yend=y2 + gradient * (xend-x2); xgap= fpart(x2 + .5)
xpx12=xend; ypx12=floor(yend)
call plotXY xpx12, ypx12 , brite(1 - fpart(yend*xgap)), switchXY
call plotXY xpx12, ypx12+1, brite( fpart(yend*xgap)), switchXY
do x=xpx11+1 to xpx12-1 /*◄═════════════════draw the line.═════════════*/
!intery=floor(intery)
call plotXY x, !intery , brite(1 - fpart(intery)), switchXY
call plotXY x, !intery+1, brite( fpart(intery)), switchXY
intery=intery + gradient
end /*x*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/ brite: return substr(background || plotC, 1 + round( abs( arg(1) ) * length(plotC)), 1) floor: parse arg #; _=trunc(#); return _ - (#<0) * (#\=_) fpart: parse arg #; return abs(# - trunc(#) ) round: return format(arg(1), , word(arg(2) 0, 1) ) /*──────────────────────────────────────────────────────────────────────────────────────*/ plotXY: parse arg xx,yy,bc,switchYX; if switchYX then parse arg yy,xx
image.xx.yy=bc; minX=min(minX, xx); maxX=max(maxX,xx)
minY=min(minY, yy); maxY=max(maxY,yy); return</lang>
- output when using the default inputs:
····│··············· ····│··············· ····│··············· ····│··········█···· ····│·········█····· ····│········█······ ····│·······█······· ····│······█········ ····│·····█········· ····│····█·········· ····│···█··········· ····│··█············ ····│·█············· ····│█·············· ····│··············· ────┼─────────────── ····│··············· ····│···············
Ruby
<lang ruby>def ipart(n); n.truncate; end def fpart(n); n - ipart(n); end def rfpart(n); 1.0 - fpart(n); end
class Pixmap
def draw_line_antialised(p1, p2, colour)
x1, y1 = p1.x, p1.y
x2, y2 = p2.x, p2.y
steep = (y2 - y1).abs > (x2 - x1).abs
if steep
x1, y1 = y1, x1
x2, y2 = y2, x2
end
if x1 > x2
x1, x2 = x2, x1
y1, y2 = y2, y1
end
deltax = x2 - x1
deltay = (y2 - y1).abs
gradient = 1.0 * deltay / deltax
# handle the first endpoint
xend = x1.round
yend = y1 + gradient * (xend - x1)
xgap = rfpart(x1 + 0.5)
xpxl1 = xend
ypxl1 = ipart(yend)
put_colour(xpxl1, ypxl1, colour, steep, rfpart(yend)*xgap)
put_colour(xpxl1, ypxl1 + 1, colour, steep, fpart(yend)*xgap)
itery = yend + gradient
# handle the second endpoint
xend = x2.round
yend = y2 + gradient * (xend - x2)
xgap = rfpart(x2 + 0.5)
xpxl2 = xend
ypxl2 = ipart(yend)
put_colour(xpxl2, ypxl2, colour, steep, rfpart(yend)*xgap)
put_colour(xpxl2, ypxl2 + 1, colour, steep, fpart(yend)*xgap)
# in between
(xpxl1 + 1).upto(xpxl2 - 1).each do |x|
put_colour(x, ipart(itery), colour, steep, rfpart(itery))
put_colour(x, ipart(itery) + 1, colour, steep, fpart(itery))
itery = itery + gradient
end
end
def put_colour(x, y, colour, steep, c) x, y = y, x if steep self[x, y] = anti_alias(colour, self[x, y], c) end
def anti_alias(new, old, ratio)
blended = new.values.zip(old.values).map {|n, o| (n*ratio + o*(1.0 - ratio)).round}
RGBColour.new(*blended)
end
end
bitmap = Pixmap.new(500, 500) bitmap.fill(RGBColour::BLUE) 10.step(430, 60) do |a|
bitmap.draw_line_antialised(Pixel[10, 10], Pixel[490,a], RGBColour::YELLOW) bitmap.draw_line_antialised(Pixel[10, 10], Pixel[a,490], RGBColour::YELLOW)
end bitmap.draw_line_antialised(Pixel[10, 10], Pixel[490,490], RGBColour::YELLOW)</lang>
Scala
Uses Bitmap#Scala. <lang Scala>import java.awt.Color import math.{floor => ipart, round, abs}
case class Point(x: Double, y: Double) {def swap = Point(y, x)}
def plotter(bm: RgbBitmap, c: Color)(x: Double, y: Double, v: Double) = {
val X = round(x).toInt
val Y = round(y).toInt
val V = v.toFloat
// tint the existing pixels
val c1 = c.getRGBColorComponents(null)
val c2 = bm.getPixel(X, Y).getRGBColorComponents(null)
val c3 = (c1 zip c2).map{case (n, o) => n * V + o * (1 - V)}
bm.setPixel(X, Y, new Color(c3(0), c3(1), c3(2)))
}
def drawLine(plotter: (Double,Double,Double) => _)(p1: Point, p2: Point) {
def fpart(x: Double) = x - ipart(x) def rfpart(x: Double) = 1 - fpart(x) def avg(a: Float, b: Float) = (a + b) / 2
val steep = abs(p2.y - p1.y) > abs(p2.x - p1.x) val (p3, p4) = if (steep) (p1.swap, p2.swap) else (p1, p2) val (a, b) = if (p3.x > p4.x) (p4, p3) else (p3, p4) val dx = b.x - a.x val dy = b.y - a.y val gradient = dy / dx var intery = 0.0
def endpoint(xpxl: Double, yend: Double, xgap: Double) {
val ypxl = ipart(yend)
if (steep) {
plotter(ypxl, xpxl, rfpart(yend) * xgap)
plotter(ypxl+1, xpxl, fpart(yend) * xgap)
} else {
plotter(xpxl, ypxl , rfpart(yend) * xgap)
plotter(xpxl, ypxl+1, fpart(yend) * xgap)
}
}
// handle first endpoint
var xpxl1 = round(a.x);
{
val yend = a.y + gradient * (xpxl1 - a.x)
val xgap = rfpart(a.x + 0.5)
endpoint(xpxl1, yend, xgap)
intery = yend + gradient
}
// handle second endpoint
val xpxl2 = round(b.x);
{
val yend = b.y + gradient * (xpxl2 - b.x)
val xgap = fpart(b.x + 0.5)
endpoint(xpxl2, yend, xgap)
}
// main loop
for (x <- (xpxl1 + 1) to (xpxl2 - 1)) {
if (steep) {
plotter(ipart(intery) , x, rfpart(intery))
plotter(ipart(intery)+1, x, fpart(intery))
} else {
plotter(x, ipart (intery), rfpart(intery))
plotter(x, ipart (intery)+1, fpart(intery))
}
intery = intery + gradient
}
}</lang> Example:
Test line drawing in various directions including vertical, horizontal, 45° and oblique (such lines are drawn multiple times to test swapped parameters). <lang Scala>val r = 120 val img = new RgbBitmap(r*2+1, r*2+1) val line = drawLine(plotter(img, Color.GRAY)_)_ img.fill(Color.WHITE) for (angle <- 0 to 360 by 30; θ = math toRadians angle; θ2 = θ + math.Pi) {
val a = Point(r + r * math.sin(θ), r + r * math.cos(θ)) val b = Point(r + r * math.sin(θ2), r + r * math.cos(θ2)) line(a, b)
} javax.imageio.ImageIO.write(img.image, "png", new java.io.File("XiaolinWuLineAlgorithm.png"))</lang>
- Output:
View the PNG, available at the following URL because RosettaCode image uploads were disabled: https://lh5.googleusercontent.com/GxBAHV4nebuO1uiKboKc6nQmmtlJV47jPwVZnQHcbV7TKm0kjdKfKteclCfxmSdFJnSKvYYoB5I
Sidef
<lang ruby>func plot(x, y, c) {
c && printf("plot %d %d %.1f\n", x, y, c);
}
func fpart(x) {
x - int(x);
}
func rfpart(x) {
1 - fpart(x);
}
func drawLine(x0, y0, x1, y1) {
var p = plot;
if (abs(y1 - y0) > abs(x1 - x0)) {
p = {|arg| plot(arg[1, 0, 2]) };
(x0, y0, x1, y1) = (y0, x0, y1, x1);
}
if (x0 > x1) {
(x0, x1, y0, y1) = (x1, x0, y1, y0);
}
var dx = (x1 - x0); var dy = (y1 - y0); var gradient = (dy / dx);
var xends = []; var intery;
# handle the endpoints
for x,y in [[x0, y0], [x1, y1]] {
var xend = int(x + 0.5);
var yend = (y + gradient*(xend-x));
var xgap = rfpart(x + 0.5);
var x_pixel = xend;
var y_pixel = yend.int;
xends << x_pixel;
p.call(x_pixel, y_pixel , rfpart(yend) * xgap);
p.call(x_pixel, y_pixel+1, fpart(yend) * xgap);
defined(intery) && next;
# first y-intersection for the main loop
intery = (yend + gradient);
}
# main loop
range(xends[0]+1, xends[1]-1).each { |x|
p.call(x, intery.int, rfpart(intery));
p.call(x, intery.int+1, fpart(intery));
intery += gradient;
}
}
drawLine(0, 1, 10, 2);</lang>
- Output:
plot 0 1 0.5 plot 10 2 0.5 plot 1 1 0.9 plot 1 2 0.1 plot 2 1 0.8 plot 2 2 0.2 plot 3 1 0.7 plot 3 2 0.3 plot 4 1 0.6 plot 4 2 0.4 plot 5 1 0.5 plot 5 2 0.5 plot 6 1 0.4 plot 6 2 0.6 plot 7 1 0.3 plot 7 2 0.7 plot 8 1 0.2 plot 8 2 0.8 plot 9 1 0.1 plot 9 2 0.9
Swift
<lang swift>import Darwin // apply pixel of color at x,y with an OVER blend to the bitmap public func pixel(color: Color, x: Int, y: Int) {
let idx = x + y * self.width
if idx >= 0 && idx < self.bitmap.count {
self.bitmap[idx] = self.blendColors(bot: self.bitmap[idx], top: color)
}
}
// return the fractional part of a Double func fpart(_ x: Double) -> Double {
return modf(x).1
}
// reciprocal of the fractional part of a Double func rfpart(_ x: Double) -> Double {
return 1 - fpart(x)
}
// draw a 1px wide line using Xiolin Wu's antialiased line algorithm public func smoothLine(_ p0: Point, _ p1: Point) {
var x0 = p0.x, x1 = p1.x, y0 = p0.y, y1 = p1.y //swapable ptrs
let steep = abs(y1 - y0) > abs(x1 - x0)
if steep {
swap(&x0, &y0)
swap(&x1, &y1)
}
if x0 > x1 {
swap(&x0, &x1)
swap(&y0, &y1)
}
let dX = x1 - x0
let dY = y1 - y0
var gradient: Double
if dX == 0.0 {
gradient = 1.0
}
else {
gradient = dY / dX
}
// handle endpoint 1
var xend = round(x0)
var yend = y0 + gradient * (xend - x0)
var xgap = self.rfpart(x0 + 0.5)
let xpxl1 = Int(xend)
let ypxl1 = Int(yend)
// first y-intersection for the main loop
var intery = yend + gradient
if steep {
self.pixel(color: self.strokeColor.colorWithAlpha(self.rfpart(yend) * xgap), x: ypxl1, y: xpxl1)
self.pixel(color: self.strokeColor.colorWithAlpha(self.fpart(yend) * xgap), x: ypxl1 + 1, y: xpxl1)
}
else {
self.pixel(color: self.strokeColor.colorWithAlpha(self.rfpart(yend) * xgap), x: xpxl1, y: ypxl1)
self.pixel(color: self.strokeColor.colorWithAlpha(self.fpart(yend) * xgap), x: xpxl1, y: ypxl1 + 1)
}
xend = round(x1)
yend = y1 + gradient * (xend - x1)
xgap = self.fpart(x1 + 0.5)
let xpxl2 = Int(xend)
let ypxl2 = Int(yend)
// handle second endpoint
if steep {
self.pixel(color: self.strokeColor.colorWithAlpha(self.rfpart(yend) * xgap), x: ypxl2, y: xpxl2)
self.pixel(color: self.strokeColor.colorWithAlpha(self.fpart(yend) * xgap), x: ypxl2 + 1, y: xpxl2)
}
else {
self.pixel(color: self.strokeColor.colorWithAlpha(self.rfpart(yend) * xgap), x: xpxl2, y: ypxl2)
self.pixel(color: self.strokeColor.colorWithAlpha(self.fpart(yend) * xgap), x: xpxl2, y: ypxl2 + 1)
}
// main loop
if steep {
for x in xpxl1+1..<xpxl2 {
self.pixel(color: self.strokeColor.colorWithAlpha(self.rfpart(intery)), x: Int(intery), y: x)
self.pixel(color: self.strokeColor.colorWithAlpha(self.fpart(intery)), x: Int(intery) + 1, y:x)
intery += gradient
}
}
else {
for x in xpxl1+1..<xpxl2 {
self.pixel(color: self.strokeColor.colorWithAlpha(self.rfpart(intery)), x: x, y: Int(intery))
self.pixel(color: self.strokeColor.colorWithAlpha(self.fpart(intery)), x: x, y: Int(intery) + 1)
intery += gradient
}
}
} </lang>
Tcl
Uses code from Basic bitmap storage#Tcl <lang tcl>package require Tcl 8.5 package require Tk
proc ::tcl::mathfunc::ipart x {expr {int($x)}} proc ::tcl::mathfunc::fpart x {expr {$x - int($x)}} proc ::tcl::mathfunc::rfpart x {expr {1.0 - fpart($x)}}
proc drawAntialiasedLine {image colour p1 p2} {
lassign $p1 x1 y1 lassign $p2 x2 y2
set steep [expr {abs($y2 - $y1) > abs($x2 - $x1)}]
if {$steep} {
lassign [list $x1 $y1] y1 x1
lassign [list $x2 $y2] y2 x2
}
if {$x1 > $x2} {
lassign [list $x1 $x2] x2 x1
lassign [list $y1 $y2] y2 y1
}
set deltax [expr {$x2 - $x1}]
set deltay [expr {abs($y2 - $y1)}]
set gradient [expr {1.0 * $deltay / $deltax}]
# handle the first endpoint
set xend [expr {round($x1)}]
set yend [expr {$y1 + $gradient * ($xend - $x1)}]
set xgap [expr {rfpart($x1 + 0.5)}]
set xpxl1 $xend
set ypxl1 [expr {ipart($yend)}]
plot $image $colour $steep $xpxl1 $ypxl1 [expr {rfpart($yend)*$xgap}]
plot $image $colour $steep $xpxl1 [expr {$ypxl1+1}] [expr {fpart($yend)*$xgap}]
set itery [expr {$yend + $gradient}]
# handle the second endpoint
set xend [expr {round($x2)}]
set yend [expr {$y2 + $gradient * ($xend - $x2)}]
set xgap [expr {rfpart($x2 + 0.5)}]
set xpxl2 $xend
set ypxl2 [expr {ipart($yend)}]
plot $image $colour $steep $xpxl2 $ypxl2 [expr {rfpart($yend)*$xgap}]
plot $image $colour $steep $xpxl2 [expr {$ypxl2+1}] [expr {fpart($yend)*$xgap}]
for {set x [expr {$xpxl1 + 1}]} {$x < $xpxl2} {incr x} {
plot $image $colour $steep $x [expr {ipart($itery)}] [expr {rfpart($itery)}]
plot $image $colour $steep $x [expr {ipart($itery) + 1}] [expr {fpart($itery)}]
set itery [expr {$itery + $gradient}]
}
}
proc plot {image colour steep x y c} {
set point [expr {$steep ? [list $y $x] : [list $x $y]}]
set newColour [antialias $colour [getPixel $image $point] $c]
setPixel $image $newColour $point
}
proc antialias {newColour oldColour c} {
# get the new colour r,g,b
if {[scan $newColour "#%2x%2x%2x%c" nr ng gb -] != 3} {
scan [colour2rgb $newColour] "#%2x%2x%2x" nr ng nb
}
# get the current colour r,g,b
scan $oldColour "#%2x%2x%2x" cr cg cb
# blend the colours in the ratio defined by "c"
foreach new [list $nr $ng $nb] curr [list $cr $cg $cb] {
append blend [format {%02x} [expr {round($new*$c + $curr*(1.0-$c))}]]
}
return #$blend
}
proc colour2rgb {color_name} {
foreach part [winfo rgb . $color_name] {
append colour [format %02x [expr {$part >> 8}]]
}
return #$colour
}
set img [newImage 500 500] fill $img blue for {set a 10} {$a < 500} {incr a 60} {
drawAntialiasedLine $img yellow {10 10} [list 490 $a]
drawAntialiasedLine $img yellow {10 10} [list $a 490]
} toplevel .wu label .wu.l -image $img pack .wu.l</lang>
Yabasic
<lang Yabasic>bresline = false // space toggles, for comparison
rB = 255 : gB = 255 : bB = 224 rL = 0 : gL = 0 : bL = 255
sub round(x)
return int(x + .5)
end sub
sub plot(x, y, c, steep) // plot the pixel at (x, y) with brightness c (where 0 <= c <= 1)
local t, C if steep then t = x : x = y : y = t end if C = 1 - c color rL * c + rB * C, gL * c + gB * C, bL * c + bB * C dot x, y
end sub
sub plot2(x, y, f, xgap, steep)
plot(x, y, (1 - f) * xgap, steep) plot(x, y + 1, f * xgap, steep)
end sub
sub draw_line(x0, y0, x1, y1)
local steep, t, dx, dy, gradient, xend, yend, xgap, xpxl1, ypxl1, xpxl2, ypxl2, intery
if bresline then
line x0, y0, x1, y1
return
end if
steep = abs(y1 - y0) > abs(x1 - x0)
if steep then
t = x0 : x0 = y0 : y0 = t
t = x1 : x1 = y1 : y1 = t
end if
if x0 > x1 then
t = x0 : x0 = x1 : x1 = t
t = y0 : y0 = y1 : y1 = t
end if
dx = x1 - x0
dy = y1 - y0
if dx = 0 then
gradient = 1
else
gradient = dy / dx
end if
// handle first endpoint
xend = round(x0)
yend = y0 + gradient * (xend - x0)
xgap = 1 - frac(x0 + 0.5)
xpxl1 = xend // this will be used in the main loop
ypxl1 = int(yend)
plot2(xpxl1, ypxl1, frac(yend), xgap, steep)
intery = yend + gradient // first y-intersection for the main loop
// handle second endpoint
xend = round(x1)
yend = y1 + gradient * (xend - x1)
xgap = frac(x1 + 0.5)
xpxl2 = xend // this will be used in the main loop
ypxl2 = int(yend)
plot2(xpxl2, ypxl2, frac(yend), xgap, steep)
// main loop
for x = xpxl1 + 1 to xpxl2 - 1
plot2(x, int(intery), frac(intery), 1, steep)
intery = intery + gradient
next x
end sub
w = 640 : h = 480 open window w, h
color 0, 0, 255
draw_line(0, 0, 200, 200) draw_line(w, 0, 200, 200) draw_line(0, h, 200, 200) draw_line(w, h, 200, 200)</lang>