You are encouraged to solve this task according to the task description, using any language you may know.

Using the data storage type defined on this page for raster images, and the draw_line function defined in this one, draw a quadratic bezier curve (definition on Wikipedia).

`procedure Quadratic_Bezier          (  Picture    : in out Image;             P1, P2, P3 : Point;             Color      : Pixel;             N          : Positive := 20          )  is   Points : array (0..N) of Point;begin   for I in Points'Range loop      declare         T : constant Float := Float (I) / Float (N);         A : constant Float := (1.0 - T)**2;         B : constant Float := 2.0 * T * (1.0 - T);         C : constant Float := T**2;      begin         Points (I).X := Positive (A * Float (P1.X) + B * Float (P2.X) + C * Float (P3.X));         Points (I).Y := Positive (A * Float (P1.Y) + B * Float (P2.Y) + C * Float (P3.Y));      end;   end loop;   for I in Points'First..Points'Last - 1 loop      Line (Picture, Points (I), Points (I + 1), Color);   end loop;end Quadratic_Bezier;`

The following test

`   X : Image (1..16, 1..16);begin   Fill (X, White);   Quadratic_Bezier (X, (8, 2), (13, 8), (2, 15), Black);   Print (X);`

should produce;

```              H
H
H
H
H
HH
HH      H
HH  HHH
HH

```

## BBC BASIC

`      Width% = 200      Height% = 200       REM Set window size:      VDU 23,22,Width%;Height%;8,16,16,128       REM Draw quadratic Bézier curve:      PROCbezierquad(10,100, 250,270, 150,20, 20, 0,0,0)      END       DEF PROCbezierquad(x1,y1,x2,y2,x3,y3,n%,r%,g%,b%)      LOCAL i%, t, t1, a, b, c, p{()}      DIM p{(n%) x%,y%}       FOR i% = 0 TO n%        t = i% / n%        t1 = 1 - t        a = t1^2        b = 2 * t * t1        c = t^2        p{(i%)}.x% = INT(a * x1 + b * x2 + c * x3 + 0.5)        p{(i%)}.y% = INT(a * y1 + b * y2 + c * y3 + 0.5)      NEXT       FOR i% = 0 TO n%-1        PROCbresenham(p{(i%)}.x%,p{(i%)}.y%,p{(i%+1)}.x%,p{(i%+1)}.y%, \        \             r%,g%,b%)      NEXT      ENDPROC       DEF PROCbresenham(x1%,y1%,x2%,y2%,r%,g%,b%)      LOCAL dx%, dy%, sx%, sy%, e      dx% = ABS(x2% - x1%) : sx% = SGN(x2% - x1%)      dy% = ABS(y2% - y1%) : sy% = SGN(y2% - y1%)      IF dx% < dy% e = dx% / 2 ELSE e = dy% / 2      REPEAT        PROCsetpixel(x1%,y1%,r%,g%,b%)        IF x1% = x2% IF y1% = y2% EXIT REPEAT        IF dx% > dy% THEN          x1% += sx% : e -= dy% : IF e < 0 e += dx% : y1% += sy%        ELSE          y1% += sy% : e -= dx% : IF e < 0 e += dy% : x1% += sx%        ENDIF      UNTIL FALSE      ENDPROC       DEF PROCsetpixel(x%,y%,r%,g%,b%)      COLOUR 1,r%,g%,b%      GCOL 1      LINE x%*2,y%*2,x%*2,y%*2      ENDPROC`

## C

Interface (to be added to all other to make the final imglib.h):

`void quad_bezier(        image img,        unsigned int x1, unsigned int y1,        unsigned int x2, unsigned int y2,        unsigned int x3, unsigned int y3,        color_component r,        color_component g,        color_component b );`

Implementation:

`#include <math.h> /* number of segments for the curve */#define N_SEG 20 #define plot(x, y) put_pixel_clip(img, x, y, r, g, b)#define line(x0,y0,x1,y1) draw_line(img, x0,y0,x1,y1, r,g,b) void quad_bezier(        image img,        unsigned int x1, unsigned int y1,        unsigned int x2, unsigned int y2,        unsigned int x3, unsigned int y3,        color_component r,        color_component g,        color_component b ){    unsigned int i;    double pts[N_SEG+1][2];    for (i=0; i <= N_SEG; ++i)    {        double t = (double)i / (double)N_SEG;        double a = pow((1.0 - t), 2.0);        double b = 2.0 * t * (1.0 - t);        double c = pow(t, 2.0);        double x = a * x1 + b * x2 + c * x3;        double y = a * y1 + b * y2 + c * y3;        pts[i][0] = x;        pts[i][1] = y;    } #if 0    /* draw only points */    for (i=0; i <= N_SEG; ++i)    {        plot( pts[i][0],              pts[i][1] );    }#else    /* draw segments */    for (i=0; i < N_SEG; ++i)    {        int j = i + 1;        line( pts[i][0], pts[i][1],              pts[j][0], pts[j][1] );    }#endif}#undef plot#undef line`

## D

This solution uses two modules, from the Grayscale image and the Bresenham's line algorithm Tasks.

`import grayscale_image, bitmap_bresenhams_line_algorithm; struct Pt { int x, y; } // Signed. void quadraticBezier(size_t nSegments=20, Color)                    (Image!Color im, in Pt p1, in Pt p2, in Pt p3,                     in Color color)pure nothrow @nogc if (nSegments > 0) {    Pt[nSegments + 1] points = void;     foreach (immutable i, ref p; points) {        immutable double t = i / double(nSegments),                         a = (1.0 - t) ^^ 2,                         b = 2.0 * t * (1.0 - t),                         c = t ^^ 2;        p = Pt(cast(typeof(Pt.x))(a * p1.x + b * p2.x + c * p3.x),               cast(typeof(Pt.y))(a * p1.y + b * p2.y + c * p3.y));    }     foreach (immutable i, immutable p; points[0 .. \$ - 1])        im.drawLine(p.x, p.y, points[i + 1].x, points[i + 1].y, color);} void main() {    auto im = new Image!Gray(20, 20);    im.clear(Gray.white);    im.quadraticBezier(Pt(1,10), Pt(25,27), Pt(15,2), Gray.black);    im.textualShow();}`
Output:
```....................
....................
...............#....
...............#....
...............#....
................#...
................#...
.................#..
.................#..
.................#..
.#...............#..
..##.............#..
....##...........#..
......#..........#..
.......#.........#..
........###......#..
...........######...
....................
....................
....................```

## FBSL

Windows' graphics origin is located at the bottom-left corner of device bitmap.

Translation of BBC BASIC using pure FBSL's built-in graphics functions:

`#DEFINE WM_LBUTTONDOWN 513#DEFINE WM_CLOSE 16 FBSLSETTEXT(ME, "Bezier Quadratic")FBSLSETFORMCOLOR(ME, RGB(0, 255, 255)) ' Cyan: persistent background colorDRAWWIDTH(5) ' Adjust point sizeFBSL.GETDC(ME) ' Use volatile FBSL.GETDC below to avoid extra assignments RESIZE(ME, 0, 0, 235, 235)CENTER(ME)SHOW(ME) DIM Height AS INTEGERFBSL.GETCLIENTRECT(ME, 0, 0, 0, Height) BEGIN EVENTS	SELECT CASE CBMSG		CASE WM_LBUTTONDOWN: BezierQuad(10, 100, 250, 270, 150, 20, 20) ' Draw		CASE WM_CLOSE: FBSL.RELEASEDC(ME, FBSL.GETDC) ' Clean up	END SELECTEND EVENTS SUB BezierQuad(x1, y1, x2, y2, x3, y3, n)	TYPE POINTAPI		x AS INTEGER		y AS INTEGER	END TYPE 	DIM t, t1, a, b, c, p[n] AS POINTAPI 	FOR DIM i = 0 TO n		t = i / n: t1 = 1 - t		a = t1 ^ 2		b = 2 * t * t1		c = t ^ 2		p[i].x = a * x1 + b * x2 + c * x3 + 0.5		p[i].y = Height - (a * y1 + b * y2 + c * y3 + 0.5)	NEXT 	FOR i = 0 TO n - 1		Bresenham(p[i].x, p[i].y, p[i + 1].x, p[i + 1].y)	NEXT 	SUB Bresenham(x0, y0, x1, y1)		DIM dx = ABS(x0 - x1), sx = SGN(x0 - x1)		DIM dy = ABS(y0 - y1), sy = SGN(y0 - y1)		DIM tmp, er = IIF(dx > dy, dx, -dy) / 2 		WHILE NOT (x0 = x1 ANDALSO y0 = y1)			PSET(FBSL.GETDC, x0, y0, &HFF) ' Red: Windows stores colors in BGR order			tmp = er			IF tmp > -dx THEN: er = er - dy: x0 = x0 + sx: END IF			IF tmp < +dy THEN: er = er + dx: y0 = y0 + sy: END IF		WEND	END SUBEND SUB`

Output:

## Factor

Some code is shared with the cubic bezier task, but I put it here again to make it simple (hoping the two version don't diverge) Same remark as with cubic bezier, the points could go into a sequence to simplify stack shuffling

`USING: arrays kernel locals math math.functions rosettacode.raster.storage sequences ;IN: rosettacode.raster.line ! This gives a function:: (quadratic-bezier) ( P0 P1 P2 -- bezier )    [ :> x         1 x - sq P0 n*v        2 1 x - x * * P1 n*v        x sq P2 n*v        v+ v+ ] ; inline ! Same code from the cubic bezier task: t-interval ( x -- interval )    [ iota ] keep 1 - [ / ] curry map ;: points-to-lines ( seq -- seq )    dup rest [ 2array ] 2map ;: draw-lines ( {R,G,B} points image -- )     [ [ first2 ] dip draw-line ] curry with each ;:: bezier-lines ( {R,G,B} P0 P1 P2 image -- )    100 t-interval P0 P1 P2 (quadratic-bezier) map    points-to-lines    {R,G,B} swap image draw-lines ; `

## Fortran

Works with: Fortran version 90 and later

(This subroutine must be inside the `RCImagePrimitive` module, see here)

`subroutine quad_bezier(img, p1, p2, p3, color)  type(rgbimage), intent(inout) :: img  type(point), intent(in) :: p1, p2, p3  type(rgb), intent(in) :: color   integer :: i, j  real :: pts(0:N_SEG,0:1), t, a, b, c, x, y   do i = 0, N_SEG     t = real(i) / real(N_SEG)     a = (1.0 - t)**2.0     b = 2.0 * t * (1.0 - t)     c = t**2.0     x = a * p1%x + b * p2%x + c * p3%x      y = a * p1%y + b * p2%y + c * p3%y      pts(i,0) = x     pts(i,1) = y  end do   do i = 0, N_SEG-1     j = i + 1     call draw_line(img, point(pts(i,0), pts(i,1)), &                    point(pts(j,0), pts(j,1)), color)  end do end subroutine quad_bezier`

## FreeBASIC

Translation of: BBC BASIC
`' version 01-11-2016' compile with: fbc -s console ' translation from Bitmap/Bresenham's line algorithm C entrySub Br_line(x0 As Integer, y0 As Integer, x1 As Integer, y1 As Integer, _                                            Col As UInteger = &HFFFFFF)     Dim As Integer dx = Abs(x1 - x0), dy = Abs(y1 - y0)    Dim As Integer sx = IIf(x0 < x1, 1, -1)    Dim As Integer sy = IIf(y0 < y1, 1, -1)    Dim As Integer er = IIf(dx > dy, dx, -dy) \ 2, e2     Do        PSet(x0, y0), col        If (x0 = x1) And (y0 = y1) Then Exit Do        e2 = er        If e2 > -dx Then Er -= dy : x0 += sx        If e2 <  dy Then Er += dx : y0 += sy    Loop End Sub ' Bitmap/Bézier curves/Quadratic BBC BASIC entrySub bezierquad(x1 As Double, y1 As Double, x2 As Double, y2 As Double, _    x3 As Double, y3 As Double, n As ULong, col As UInteger = &HFFFFFF)     Type point_        x As Integer        y As Integer    End Type     Dim As ULong i    Dim As Double t, t1, a, b, c, d    Dim As point_ p(n)     For i = 0 To n        t = i / n        t1 = 1 - t        a = t1 ^ 2        b = t * t1 * 2        c = t ^ 2        p(i).x = Int(a * x1 + b * x2  + c * x3 + .5)        p(i).y = Int(a * y1 + b * y2  + c * y3 + .5)    Next     For i = 0 To n -1        Br_line(p(i).x, p(i).y, p(i +1).x, p(i +1).y, col)    Next End Sub ' ------=< MAIN >=------ ScreenRes 250, 250, 32  ' 0,0 in top left corner bezierquad(10, 100, 250, 270, 150, 20, 20)  ' empty keyboard bufferWhile InKey <> "" : WendPrint : Print "hit any key to end program"SleepEnd`

## Go

Translation of: C
`package raster const b2Seg = 20 func (b *Bitmap) Bézier2(x1, y1, x2, y2, x3, y3 int, p Pixel) {    var px, py [b2Seg + 1]int    fx1, fy1 := float64(x1), float64(y1)    fx2, fy2 := float64(x2), float64(y2)    fx3, fy3 := float64(x3), float64(y3)    for i := range px {        c := float64(i) / b2Seg        a := 1 - c        a, b, c := a*a, 2 * c * a, c*c        px[i] = int(a*fx1 + b*fx2 + c*fx3)        py[i] = int(a*fy1 + b*fy2 + c*fy3)    }    x0, y0 := px[0], py[0]    for i := 1; i <= b2Seg; i++ {        x1, y1 := px[i], py[i]        b.Line(x0, y0, x1, y1, p)        x0, y0 = x1, y1    }} func (b *Bitmap) Bézier2Rgb(x1, y1, x2, y2, x3, y3 int, c Rgb) {    b.Bézier2(x1, y1, x2, y2, x3, y3, c.Pixel())}`

Demonstration program:

`package main import (    "fmt"    "raster") func main() {    b := raster.NewBitmap(400, 300)    b.FillRgb(0xdfffef)    b.Bézier2Rgb(20, 150, 500, -100, 300, 280, raster.Rgb(0x3f8fef))    if err := b.WritePpmFile("bez2.ppm"); err != nil {        fmt.Println(err)    }}`

`{-# LANGUAGE    FlexibleInstances, TypeSynonymInstances,    ViewPatterns #-} import Bitmapimport Bitmap.Lineimport Control.Monadimport Control.Monad.ST type Point = (Double, Double)fromPixel (Pixel (x, y)) = (toEnum x, toEnum y)toPixel (x, y) = Pixel (round x, round y) pmap :: (Double -> Double) -> Point -> Pointpmap f (x, y) = (f x, f y) onCoordinates :: (Double -> Double -> Double) -> Point -> Point -> PointonCoordinates f (xa, ya) (xb, yb) = (f xa xb, f ya yb) instance Num Point where    (+) = onCoordinates (+)    (-) = onCoordinates (-)    (*) = onCoordinates (*)    negate = pmap negate    abs = pmap abs    signum = pmap signum    fromInteger i = (i', i')      where i' = fromInteger i bézier :: Color c =>    Image s c -> Pixel -> Pixel -> Pixel -> c -> Int ->    ST s ()bézier  i  (fromPixel -> p1) (fromPixel -> p2) (fromPixel -> p3)  c samples =    zipWithM_ f ts (tail ts)  where ts = map (/ top) [0 .. top]          where top = toEnum \$ samples - 1        curvePoint t =            pt (t' ^^ 2) p1 +            pt (2 * t * t') p2 +            pt (t ^^ 2) p3          where t' = 1 - t                pt n p = pmap (*n) p        f (curvePoint -> p1) (curvePoint -> p2) =            line i (toPixel p1) (toPixel p2) c`

## J

See Cubic bezier curves for a generalized solution.

## Julia

See Cubic bezier curves#Julia for a generalized solution.

## Kotlin

This incorporates code from other relevant tasks in order to provide a runnable example.

`// Version 1.2.40 import java.awt.Colorimport java.awt.Graphicsimport java.awt.image.BufferedImageimport kotlin.math.absimport java.io.Fileimport javax.imageio.ImageIO class Point(var x: Int, var y: Int) class BasicBitmapStorage(width: Int, height: Int) {    val image = BufferedImage(width, height, BufferedImage.TYPE_3BYTE_BGR)     fun fill(c: Color) {        val g = image.graphics        g.color = c        g.fillRect(0, 0, image.width, image.height)    }     fun setPixel(x: Int, y: Int, c: Color) = image.setRGB(x, y, c.getRGB())     fun getPixel(x: Int, y: Int) = Color(image.getRGB(x, y))     fun drawLine(x0: Int, y0: Int, x1: Int, y1: Int, c: Color) {        val dx = abs(x1 - x0)        val dy = abs(y1 - y0)        val sx = if (x0 < x1) 1 else -1        val sy = if (y0 < y1) 1 else -1        var xx = x0        var yy = y0        var e1 = (if (dx > dy) dx else -dy) / 2        var e2: Int        while (true) {            setPixel(xx, yy, c)            if (xx == x1 && yy == y1) break            e2 = e1            if (e2 > -dx) { e1 -= dy; xx += sx }            if (e2 <  dy) { e1 += dx; yy += sy }        }    }     fun quadraticBezier(p1: Point, p2: Point, p3: Point, clr: Color, n: Int) {        val pts = List(n + 1) { Point(0, 0) }        for (i in 0..n) {            val t = i.toDouble() / n            val u = 1.0 - t            val a = u * u            val b = 2.0 * t * u            val c = t * t            pts[i].x = (a * p1.x + b * p2.x + c * p3.x).toInt()            pts[i].y = (a * p1.y + b * p2.y + c * p3.y).toInt()            setPixel(pts[i].x, pts[i].y, clr)        }        for (i in 0 until n) {            val j = i + 1            drawLine(pts[i].x, pts[i].y, pts[j].x, pts[j].y, clr)        }    }} fun main(args: Array<String>) {    val width = 320    val height = 320    val bbs = BasicBitmapStorage(width, height)    with (bbs) {        fill(Color.cyan)        val p1 = Point(10, 100)        val p2 = Point(250, 270)        val p3 = Point(150, 20)        quadraticBezier(p1, p2, p3, Color.black, 20)        val qbFile = File("quadratic_bezier.jpg")        ImageIO.write(image, "jpg", qbFile)    }}`

## Mathematica / Wolfram Language

`pts = {{0, 0}, {1, -1}, {2, 1}};Graphics[{BSplineCurve[pts], Green, Line[pts], Red, Point[pts]}]`

Second solution using built-in function BezierCurve.

`pts = {{0, 0}, {1, -1}, {2, 1}};Graphics[{BezierCurve[pts], Green, Line[pts], Red, Point[pts]}]`

## MATLAB

Note: Store this function in a file named "bezierQuad.mat" in the @Bitmap folder for the Bitmap class defined here.

` function bezierQuad(obj,pixel_0,pixel_1,pixel_2,color,varargin)     if( isempty(varargin) )        resolution = 20;    else        resolution = varargin{1};    end     %Calculate time axis    time = (0:1/resolution:1)';    timeMinus = 1-time;     %The formula for the curve is expanded for clarity, the lack of    %loops is because its calculation has been vectorized    curve = (timeMinus.^2)*pixel_0; %First term of polynomial    curve = curve + (2.*time.*timeMinus)*pixel_1; %second term of polynomial    curve = curve + (time.^2)*pixel_2; %third term of polynomial     curve = round(curve); %round each of the points to the nearest integer     %connect each of the points in the curve with a line using the    %Bresenham Line algorithm    for i = (1:length(curve)-1)        obj.bresenhamLine(curve(i,:),curve(i+1,:),color);    end     assignin('caller',inputname(1),obj); %saves the changes to the object end `

Sample usage: This will generate the image example for the Go solution.

` >> img = Bitmap(400,300);>> img.fill([223 255 239]);>> img.bezierQuad([20 150],[500 -100],[300 280],[63 143 239],21);>> disp(img) `

## OCaml

`let quad_bezier ~img ~color        ~p1:(_x1, _y1)        ~p2:(_x2, _y2)        ~p3:(_x3, _y3) =  let (x1, y1, x2, y2, x3, y3) =    (float _x1, float _y1, float _x2, float _y2, float _x3, float _y3)  in  let bz t =    let a = (1.0 -. t) ** 2.0    and b = 2.0 *. t *. (1.0 -. t)    and c = t ** 2.0    in    let x = a *. x1 +. b *. x2 +. c *. x3    and y = a *. y1 +. b *. y2 +. c *. y3    in    (int_of_float x, int_of_float y)  in  let rec loop _t acc =    if _t > 20 then acc else    begin      let t = (float _t) /. 20.0 in      let x, y = bz t in      loop (succ _t) ((x,y)::acc)    end  in  let pts = loop 0 [] in   (*  (* draw only points *)  List.iter (fun (x, y) -> put_pixel img color x y) pts;  *)   (* draw segments *)  let line = draw_line ~img ~color in  let by_pair li f =    ignore (List.fold_left (fun prev x -> f prev x; x) (List.hd li) (List.tl li))  in  by_pair pts (fun p0 p1 -> line ~p0 ~p1);;;`

## Perl 6

Works with: Rakudo version 2017.09

Uses pieces from Bitmap, and Bresenham's line algorithm tasks. They are included here to make a complete, runnable program.

`class Pixel { has UInt (\$.R, \$.G, \$.B) }class Bitmap {    has UInt (\$.width, \$.height);    has Pixel @!data;     method fill(Pixel \$p) {        @!data = \$p.clone xx (\$!width*\$!height)    }    method pixel(	  \$i where ^\$!width,	  \$j where ^\$!height	  --> Pixel    ) is rw { @!data[\$i + \$j * \$!width] }     method set-pixel (\$i, \$j, Pixel \$p) {        return if \$j >= \$!height;        self.pixel(\$i, \$j) = \$p.clone;    }    method get-pixel (\$i, \$j) returns Pixel {	    self.pixel(\$i, \$j);    }     method line((\$x0 is copy, \$y0 is copy), (\$x1 is copy, \$y1 is copy), \$pix) {        my \$steep = abs(\$y1 - \$y0) > abs(\$x1 - \$x0);        if \$steep {            (\$x0, \$y0) = (\$y0, \$x0);            (\$x1, \$y1) = (\$y1, \$x1);        }        if \$x0 > \$x1 {            (\$x0, \$x1) = (\$x1, \$x0);            (\$y0, \$y1) = (\$y1, \$y0);        }        my \$Δx = \$x1 - \$x0;        my \$Δy = abs(\$y1 - \$y0);        my \$error = 0;        my \$Δerror = \$Δy / \$Δx;        my \$y-step = \$y0 < \$y1 ?? 1 !! -1;        my \$y = \$y0;        for \$x0 .. \$x1 -> \$x {            if \$steep {                self.set-pixel(\$y, \$x, \$pix);            } else {                self.set-pixel(\$x, \$y, \$pix);            }            \$error += \$Δerror;            if \$error >= 0.5 {                \$y += \$y-step;                \$error -= 1.0;            }        }    }     method dot ((\$px, \$py), \$pix, \$radius = 2) {        for \$px - \$radius .. \$px + \$radius -> \$x {            for \$py - \$radius .. \$py + \$radius -> \$y {                self.set-pixel(\$x, \$y, \$pix) if ( \$px - \$x + (\$py - \$y) * i ).abs <= \$radius;            }        }    }     method quadratic ( (\$x1, \$y1), (\$x2, \$y2), (\$x3, \$y3), \$pix, \$segments = 30 ) {        my @line-segments = map -> \$t {            my \a = (1-\$t)²;            my \b = \$t * (1-\$t) * 2;            my \c = \$t²;            (a*\$x1 + b*\$x2 + c*\$x3).round(1),(a*\$y1 + b*\$y2 + c*\$y3).round(1)        }, (0, 1/\$segments, 2/\$segments ... 1);        for @line-segments.rotor(2=>-1) -> (\$p1, \$p2) { self.line( \$p1, \$p2, \$pix) };    }     method data { @!data }} role PPM {    method P6 returns Blob {	"P6\n{self.width} {self.height}\n255\n".encode('ascii')	~ Blob.new: flat map { .R, .G, .B }, self.data    }} sub color( \$r, \$g, \$b) { Pixel.new(R => \$r, G => \$g, B => \$b) } my Bitmap \$b = Bitmap.new( width => 600, height => 400) but PPM; \$b.fill( color(2,2,2) ); my @points = (65,25), (85,380), (570,15); my %seen;my \$c = 0;for @points.permutations -> @this {    %seen{@this.reverse.join.Str}++;    next if %seen{@this.join.Str};    \$b.quadratic( |@this, color(255-\$c,127,\$c+=80) );} @points.map: { \$b.dot( \$_, color(255,0,0), 3 )} \$*OUT.write: \$b.P6;`

See example image here, (converted to a .png as .ppm format is not widely supported).

## Phix

Output similar to Mathematica Requires new_image() from Bitmap, bresLine() from Bresenham's_line_algorithm, write_ppm() from Write_a_PPM_file. Included as demo\rosetta\Bitmap_BezierQuadratic.exw, results may be verified with demo\rosetta\viewppm.exw

`function quadratic_bezier(sequence img, atom x1, atom y1, atom x2, atom y2, atom x3, atom y3, integer colour, integer segments)atom t, t1, a, b, csequence pts = repeat(0,segments*2)     for i=0 to segments*2-1 by 2 do        t = i/segments        t1 = 1-t        a = power(t1,2)        b = 2*t*t1        c = power(t,2)        pts[i+1] = floor(a*x1+b*x2+c*x3)        pts[i+2] = floor(a*y1+b*y2+c*y3)    end for    for i=1 to segments*2-2 by 2 do        img = bresLine(img, pts[i], pts[i+1], pts[i+2], pts[i+3], colour)    end for    return imgend function sequence img = new_image(200,200,black)    img = quadratic_bezier(img, 0,100, 100,200, 200,0, white, 40)    img = bresLine(img,0,100,100,200,green)    img = bresLine(img,100,200,200,0,green)    img[1][100] = red    img[100][200] = red    img[200][1] = red    write_ppm("BézierQ.ppm",img)`

## PicoLisp

This uses the 'brez' line drawing function from Bitmap/Bresenham's line algorithm#PicoLisp.

`(scl 6) (de quadBezier (Img N X1 Y1 X2 Y2 X3 Y3)   (let (R (* N N)  X X1  Y Y1  DX 0  DY 0)      (for I N         (let (J (- N I)  A (*/ 1.0 J J R)  B (*/ 2.0 I J R)  C (*/ 1.0 I I R))            (brez Img X Y               (setq DX (- (+ (*/ A X1 1.0) (*/ B X2 1.0) (*/ C X3 1.0)) X))               (setq DY (- (+ (*/ A Y1 1.0) (*/ B Y2 1.0) (*/ C Y3 1.0)) Y)) )            (inc 'X DX)            (inc 'Y DY) ) ) ) )`

Test:

`(let Img (make (do 200 (link (need 300 0))))       # Create image 300 x 200   (quadBezier Img 12 20 100 300 -80 260 180)   (out "img.pbm"                                  # Write to bitmap file      (prinl "P1")      (prinl 300 " " 200)      (mapc prinl Img) ) ) (call 'display "img.pbm")`

## PureBasic

`Procedure quad_bezier(img, p1x, p1y, p2x, p2y, p3x, p3y, Color, n_seg)  Protected i  Protected.f T, t1, a, b, c, d  Dim pts.POINT(n_seg)   For i = 0 To n_seg    T = i / n_seg    t1 = 1.0 - T    a = Pow(t1, 2)    b = 2.0 * T * t1    c = Pow(T, 2)    pts(i)\x = a * p1x + b * p2x + c * p3x    pts(i)\y = a * p1y + b * p2y + c * p3y  Next   StartDrawing(ImageOutput(img))    FrontColor(Color)    For i = 0 To n_seg - 1      BresenhamLine(pts(i)\x, pts(i)\y, pts(i + 1)\x, pts(i + 1)\y)    Next  StopDrawing()EndProcedure Define w, h, imgw = 200: h = 200: img = 1CreateImage(img, w, h) ;img is internal id of the image OpenWindow(0, 0, 0, w, h,"Bezier curve, quadratic", #PB_Window_SystemMenu)quad_bezier(1, 80,20, 130,80, 20,150, RGB(255, 255, 255), 20)ImageGadget(0, 0, 0, w, h, ImageID(1)) Define eventRepeat  event = WaitWindowEvent()Until event = #PB_Event_CloseWindow `

## Python

See Cubic bezier curves#Python for a generalized solution.

## R

See Cubic bezier curves#R for a generalized solution.

## Racket

` #lang racket(require racket/draw) (define (draw-line dc p q)  (match* (p q) [((list x y) (list s t)) (send dc draw-line x y s t)])) (define (draw-lines dc ps)  (void   (for/fold ([p0 (first ps)]) ([p (rest ps)])     (draw-line dc p0 p)     p))) (define (int t p q)  (define ((int1 t) x0 x1) (+ (* (- 1 t) x0) (* t x1)))  (map (int1 t) p q)) (define (bezier-points p0 p1 p2)  (for/list ([t (in-range 0.0 1.0 (/ 1.0 20))])    (int t (int t p0 p1) (int t p1 p2)))) (define bm (make-object bitmap% 17 17))(define dc (new bitmap-dc% [bitmap bm]))(send dc set-smoothing 'unsmoothed)(send dc set-pen "red" 1 'solid)(draw-lines dc (bezier-points '(16 1) '(1 4) '(3 16)))bm `

## Ruby

See Cubic bezier curves#Ruby for a generalized solution.

## Tcl

See Cubic bezier curves#Tcl for a generalized solution.

## TI-89 BASIC

Note: This example does not use a user-defined image type, since that would be particularly impractical, but rather draws on the calculator's graph screen, which has essentially the same operations as an implementation of Basic bitmap storage would, except for being black-and-white.
`Define cubic(p1,p2,p3,segs) = Prgm  Local i,t,u,prev,pt  0 → pt  For i,1,segs+1    (i-1.0)/segs → t   © Decimal to avoid slow exact arithetic    (1-t) → u    pt → prev    u^2*p1 + 2*t*u*p2 + t^2*p3 → pt    If i>1 Then      PxlLine floor(prev[1,1]), floor(prev[1,2]), floor(pt[1,1]), floor(pt[1,2])    EndIf  EndForEndPrgm`

## Vedit macro language

This implementation uses de Casteljau's algorithm to recursively split the Bezier curve into two smaller segments until the segment is short enough to be approximated with a straight line. The advantage of this method is that only integer calculations are needed, and the most complex operations are addition and shift right. (I have used multiplication and division here for clarity.)

Constant recursion depth is used here. Recursion depth of 5 seems to give accurate enough result in most situations. In real world implementations, some adaptive method is often used to decide when to stop recursion.

`// Daw a Cubic bezier curve//  #20, #30 = Start point//  #21, #31 = Control point 1//  #22, #32 = Control point 2//  #23, #33 = end point//  #40 = depth of recursion :CUBIC_BEZIER:if (#40 > 0) {    #24 = (#20+#21)/2;              #34 = (#30+#31)/2    #26 = (#22+#23)/2;              #36 = (#32+#33)/2    #27 = (#20+#21*2+#22)/4;        #37 = (#30+#31*2+#32)/4    #28 = (#21+#22*2+#23)/4;        #38 = (#31+#32*2+#33)/4    #29 = (#20+#21*3+#22*3+#23)/8;  #39 = (#30+#31*3+#32*3+#33)/8    Num_Push(20,40)        #21 = #24; #31 = #34    // control 1        #22 = #27; #32 = #37    // control 2        #23 = #29; #33 = #39    // end point        #40--        Call("CUBIC_BEZIER")    // Draw "left" part    Num_Pop(20,40)    Num_Push(20,40)        #20 = #29; #30 = #39    // start point        #21 = #28; #31 = #38    // control 1        #22 = #26; #32 = #36    // control 2        #40--        Call("CUBIC_BEZIER")    // Draw "right" part    Num_Pop(20,40)} else {    #1=#20; #2=#30; #3=#23; #4=#33    Call("DRAW_LINE")}return`

## XPL0

`include c:\cxpl\codes;          \intrinsic 'code' declarations proc Bezier(P0, P1, P2);        \Draw quadratic Bezier curvereal P0, P1, P2;def  Segments = 8;int  I;real T, A, B, C, X, Y;[Move(fix(P0(0)), fix(P0(1)));for I:= 1 to Segments do        [T:= float(I)/float(Segments);        A:= sq(1.-T);        B:= 2.*T*(1.-T);        C:= sq(T);        X:= A*P0(0) + B*P1(0) + C*P2(0);        Y:= A*P0(1) + B*P1(1) + C*P2(1);        Line(fix(X), fix(Y), \$00FFFF);          \cyan line segments        ];Point(fix(P0(0)), fix(P0(1)), \$FF0000);         \red control pointsPoint(fix(P1(0)), fix(P1(1)), \$FF0000);Point(fix(P2(0)), fix(P2(1)), \$FF0000);]; [SetVid(\$112);          \set 640x480x24 video graphicsBezier([0., 0.], [80., 100.], [160., 20.]);if ChIn(1) then [];     \wait for keystrokeSetVid(3);              \restore normal text display]`

## zkl

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl

Add this to the PPM class:

`   fcn qBezier(p0x,p0y, p1x,p1y, p2x,p2y, rgb, numPts=500){      numPts.pump(Void,'wrap(t){ // B(t)      	 t=t.toFloat()/numPts; t1:=(1.0 - t);	 a:=t1*t1; b:=t*t1*2; c:=t*t;	 x:=a*p0x + b*p1x + c*p2x + 0.5;	 y:=a*p0y + b*p1y + c*p2y + 0.5;	 __sSet(rgb,x,y);      });   }`

Doesn't use line segments, they don't seem like an improvement.

`bitmap:=PPM(200,200,0xff|ff|ff);bitmap.qBezier(10,100, 250,270, 150,20, 0);bitmap.write(File("foo.ppm","wb"));`
Output:

Same as the BBC BASIC image: