B-spline: Difference between revisions
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* [https://www.cl.cam.ac.uk/teaching/2000/AGraphHCI/SMEG/node4.html B-splines]
<br><br>
=={{header|ALGOL 68}}==
{{Trans|Lua}}Which is {{Trans|Wren}}Suppresses unused parts of the plot.
<syntaxhighlight lang="algol68">
BEGIN # construct a B-Spline #
# mode to hold a B Spline #
MODE BSPLINE = STRUCT( FLEX[ 1 : 0, 1 : 2 ]INT control points
, INT n
, INT k
, FLEX[ 1 : 0 ]INT t
);
PROC uniform knot vector = ( INT lb, ub )[]INT:
BEGIN
[ lb : ub ]INT range;
FOR n FROM lb TO ub DO range[ n ] := n OD;
range
END # uniform knot vector # ;
PROC calculate bspline = ( REF BSPLINE bs, INT i, k, x )REAL:
IF k = 1
THEN ABS ( ( t OF bs )[ i ] <= x AND x < ( t OF bs )[ i + 1 ] )
ELSE
PROC helper = ( REF BSPLINE bs, INT i, k, x )REAL:
IF ( t OF bs )[ i + k ] /= ( t OF bs )[ i ]
THEN ( x - ( t OF bs )[ i ] ) / ( ( t OF bs )[ i + k ] - ( t OF bs )[ i ] )
ELSE 0
FI # helper # ;
( helper( bs, i, k - 1, x ) ) * calculate bspline( bs, i, k - 1, x )
+ ( 1 - helper( bs, i + 1, k - 1, x ) ) * calculate bspline( bs, i + 1, k - 1, x )
FI # calculate bspline # ;
PROC round = ( REAL n )INT: ENTIER( n + 0.5 );
PROC get bspline points = ( REF BSPLINE bs )[,]INT:
BEGIN
INT p from = ( t OF bs )[ k OF bs ];
INT p to = ( t OF bs )[ 1 + n OF bs ] - 1;
[ p from : p to, 1 : 2 ]INT points;
FOR x FROM p from TO p to DO
REAL sum x := 0;
REAL sum y := 0;
FOR i TO n OF bs DO
REAL f = calculate bspline( bs, i, k OF bs, x );
sum x +:= f * ( control points OF bs )[ i, 1 ];
sum y +:= f * ( control points OF bs )[ i, 2 ]
OD;
points[ x, 1 ] := round( sum x );
points[ x, 2 ] := round( sum y )
OD;
points
END # get bspline points # ;
PROC raytrace = ( INT x0, y0, x2, y2, REF[,]BOOL plot, PROC( REF[,]BOOL, INT, INT )VOID visit )VOID:
BEGIN
INT x := x0;
INT y := y0;
INT dx := ABS ( x2 - x );
INT dy := ABS ( y2 - y );
INT n = 1 + dx + dy;
INT dir x = IF x2 > x THEN 1 ELSE -1 FI;
INT dir y = IF y2 > y THEN 1 ELSE -1 FI;
INT err := dx - dy;
dx *:= 2;
dy *:= 2;
FOR i TO n DO
visit( plot, x, y );
IF err > 0
THEN x +:= dir x; err -:= dy
ELSE y +:= dir y; err +:= dx
FI
OD
END # raytrace # ;
PROC plot line = ( REF[,]BOOL plot, INT x1, y1, x2, y2 )VOID:
raytrace( x1, y1, x2, y2, plot
, ( REF[,]BOOL plot, INT x, INT y )VOID: IF x >= 0
AND y >= 0
AND x < 1 UPB plot
AND y < 2 UPB plot
THEN plot[ x + 1, y + 1 ] := TRUE
FI
);
PROC plot bspline = ( REF BSPLINE bs, REF[,]BOOL plot, REAL scale x, scale y )VOID:
IF k OF bs > n OF bs OR k OF bs < 1 THEN
print( ( "k (= ", whole( k OF bs, 0 ), ") can't be more than ", whole( n OF bs, 0 ) ) );
print( ( " or less than 1.", newline ) );
stop
ELSE
[,]INT points = get bspline points( bs );
# Plot the curve. #
FOR i FROM 1 LWB points TO 1 UPB points - 1 DO
INT p1x = points[ i, 1 ], p1y = points[ i, 2 ];
INT p2x = points[ i + 1, 1 ], p2y = points[ i + 1, 2 ];
plot line( plot
, round( p1x * scale x ), round( p1y * scale y )
, round( p2x * scale x ), round( p2y * scale y )
)
OD
FI # plot bspline # ;
# print the plot - outputs @ or blank depending on whether the point is plotted or not #
PROC print plot = ( [,]BOOL plot )VOID:
FOR row FROM 1 LWB plot
TO BEGIN # find the highest used row #
INT max row := 1 UPB plot;
WHILE IF max row < 1 LWB plot
THEN FALSE
ELSE
BOOL empty row := TRUE;
FOR column FROM 2 LWB plot TO 2 UPB plot
WHILE empty row := NOT plot[ column, max row ]
DO
SKIP
OD;
empty row
FI
DO
max row -:= 1
OD;
max row
END
DO
INT max column := 2 UPB plot;
WHILE IF max column < 2 LWB plot THEN FALSE ELSE NOT plot[ max column, row ] FI
DO
max column -:= 1
OD;
FOR column FROM 2 LWB plot TO max column DO
print( ( IF plot[ column, row ] THEN "@" ELSE " " FI ) )
OD;
print( ( newline ) )
OD # print plot # ;
# task #
[,]INT control points
= ( ( 171, 171 ), ( 185, 111 ), ( 202, 109 ), ( 202, 189 ), ( 328, 160 ), ( 208, 254 )
, ( 241, 330 ), ( 164, 252 ), ( 69, 278 ), ( 139, 208 ), ( 72, 148 ), ( 168, 172 )
);
INT k = 4; # Polynomial degree is one less than this i.e. cubic. #
BSPLINE bs := ( control points
, UPB control points
, k
, uniform knot vector( 1, UPB control points + k )
);
REAL scale x = 0.4; # Since we print the plot to the console as text let's scale things appropriately. #
REAL scale y = 0.2;
[ 1 : 350, 1 : 350 ]BOOL plot;
FOR r FROM 1 LWB plot TO 1 UPB plot DO FOR c FROM 2 LWB plot TO 2 UPB plot DO plot[ c, r ] := FALSE OD OD;
plot bspline( bs, plot, scale x, scale y );
print plot( plot )
END
</syntaxhighlight>
{{out}}
leading blank lines removed...
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</pre>
=={{header|Julia}}==
Choose BSpline D of 2, ie degree 1.
<
Point(t::Tuple) = Vec2(Float64(t[1]), Float64(t[2]))
Line 35 ⟶ 232:
(208, 254), (241, 330), (164,252), (69, 278), (139, 208), (72, 148), (168, 172)])
plt = plot(map(a -> a.x, controlpoints), map(a -> a.y, controlpoints))
savefig(plt, "BSplineplot.png")</
=={{header|Lua}}==
{{trans|Wren}}
<syntaxhighlight lang="lua">local function Range(from, to)
local range = {}
for n = from, to do table.insert(range, n) end
return range
end
local function Bspline(controlPoints, k)
return {
controlPoints = controlPoints,
n = #controlPoints,
k = k,
t = Range(1, #controlPoints+k), -- Use a uniform knot vector, delta=1.
}
end
local function helper(bspline, i, k, x)
return (bspline.t[i+k] ~= bspline.t[i])
and (x - bspline.t[i]) / (bspline.t[i+k] - bspline.t[i])
or 0
end
local function calculateBspline(bspline, i, k, x)
if k == 1 then
return (bspline.t[i] <= x and x < bspline.t[i+1]) and 1 or 0
end
return ( helper(bspline, i , k-1, x)) * calculateBspline(bspline, i , k-1, x)
+ (1-helper(bspline, i+1, k-1, x)) * calculateBspline(bspline, i+1, k-1, x)
end
local function round(n)
return math.floor(n+.5)
end
local function getBsplinePoints(bspline)
local points = {}
for x = bspline.t[bspline.k], bspline.t[bspline.n+1]-1 do
local sumX = 0
local sumY = 0
for i = 1, bspline.n do
local f = calculateBspline(bspline, i, bspline.k, x)
sumX = sumX + f * bspline.controlPoints[i].x
sumY = sumY + f * bspline.controlPoints[i].y
end
table.insert(points, {x=round(sumX), y=round(sumY)})
end
return points
end
local function Plot(unscaledWidth,unscaledHeight, scaleX,scaleY)
local plot = {
width = round(unscaledWidth * scaleX),
height = round(unscaledHeight * scaleY),
scaleX = scaleX,
scaleY = scaleY,
}
for row = 1, plot.height do
plot[row] = {}
end
return plot
end
local function raytrace(x,y, x2,y2, visit)
local dx = math.abs(x2 - x)
local dy = math.abs(y2 - y)
local n = 1 + dx + dy
local dirX = (x2 > x) and 1 or -1
local dirY = (y2 > y) and 1 or -1
local err = dx - dy
dx, dy = 2*dx, 2*dy
for n = 1, n do
visit(x, y)
if err > 0 then x, err = x+dirX, err-dy
else y, err = y+dirY, err+dx end
end
end
local function plotLine(plot, x1,y1, x2,y2)
raytrace(x1,y1, x2,y2, function(x, y)
if x >= 0 and y >= 0 and x < plot.width and y < plot.height then
plot[y+1][x+1] = true
end
end)
end
local function plotBspline(bspline, plot)
if bspline.k > bspline.n or bspline.k < 1 then
error("k (= "..bspline.k..") can't be more than "..bspline.n.." or less than 1.")
end
local points = getBsplinePoints(bspline)
-- Plot the curve.
for i = 1, #points-1 do
local p1 = points[i]
local p2 = points[i+1]
plotLine(plot,
round(p1.x*plot.scaleX), round(p1.y*plot.scaleY),
round(p2.x*plot.scaleX), round(p2.y*plot.scaleY)
)
end
end
local function printPlot(plot)
for row = 1, plot.height do
for column = 1, plot.width do
io.write(plot[row][column] and "@" or " ")
end
io.write("\n")
end
end
local controlPoints = {
{x=171, y=171}, {x=185, y=111}, {x=202, y=109}, {x=202, y=189}, {x=328, y=160}, {x=208, y=254},
{x=241, y=330}, {x=164, y=252}, {x= 69, y=278}, {x=139, y=208}, {x= 72, y=148}, {x=168, y=172},
}
local k = 4 -- Polynomial degree is one less than this i.e. cubic.
local bspline = Bspline(controlPoints, k)
local scaleX = .4 -- Since we print the plot to the console as text let's scale things appropriately.
local scaleY = .2
local plot = Plot(350,350, scaleX,scaleY)
plotBspline(bspline, plot)
printPlot(plot)</syntaxhighlight>
{{out}}
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</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<
BSplineCurve[{{171, 171}, {185, 111}, {202, 109}, {202, 189}, {328,
160}, {208, 254}, {241, 330}, {164, 252}, {69, 278}, {139,
208}, {72, 148}, {168, 172}}, SplineClosed -> True,
SplineDegree -> 2]]</
{{out}}
Outputs a graphical representation of a B-spline.
=={{header|Perl}}==
{{trans|Raku}}
<syntaxhighlight lang="perl">use strict;
use warnings;
use Class::Struct;
use Cairo;
{ package Line;
struct( A => '@', B => '@');
}
my ($WIDTH, $HEIGHT, $W_LINE, $CURVE_F, $DETACHED, $OUTPUT ) =
( 400, 400, 2, 0.25, 0, 'run/b-spline.png' );
my @pt = (
[171, 171], [185, 111], [202, 109], [202, 189], [328, 160], [208, 254],
[241, 330], [164, 252], [ 69, 278], [139, 208], [ 72, 148], [168, 172]
);
my $cnt = @pt;
sub angle {
my($g) = @_;
atan2 $g->B->[1] - $g->A->[1], $g->B->[0] - $g->A->[0]
}
sub control_points {
my($g, $l) = @_;
my $h = Line->new;
my $lgt = sqrt( ($g->B->[0] - $l->A->[0])**2 + ($g->B->[1] - $l->A->[1])**2 );
@{$h->B} = @{$l->A};
@{$h->A} = ($g->B->[0] - $lgt * cos(angle $g) , $g->B->[1] - $lgt * sin(angle $g));
my $a = angle $h;
my @p1 = ($g->B->[0] + $lgt * cos($a) * $CURVE_F, $g->B->[1] + $lgt * sin($a) * $CURVE_F);
@{$h->A} = @{$g->B};
@{$h->B} = ($l->A->[0] + $lgt * cos(angle $l) , $l->A->[1] + $lgt * sin(angle $l));
$a = angle $h;
my @p2 = ($l->A->[0] - $lgt * cos($a) * $CURVE_F, $l->A->[1] - $lgt * sin($a) * $CURVE_F);
\@p1, \@p2
}
my $surf = Cairo::ImageSurface->create ('argb32', $WIDTH, $HEIGHT);
my $cr = Cairo::Context->create ($surf);
$cr->set_line_width($W_LINE);
$cr->move_to($pt[$DETACHED - 1 + $cnt][0], $pt[$DETACHED - 1 + $cnt][1]);
my Line ($g,$l);
for my $j ($DETACHED..$cnt-1) {
$g = Line->new( A=>$pt[($j + $cnt - 2) % $cnt], B=>$pt[($j + $cnt - 1) % $cnt]);
$l = Line->new( A=>$pt[($j + $cnt + 0) % $cnt], B=>$pt[($j + $cnt + 1) % $cnt]);
my($p1,$p2) = control_points($g, $l);
$cr->curve_to($$p1[0], $$p1[1], $$p2[0], $$p2[1], $pt[$j][0], $pt[$j][1]);
}
$cr->stroke;
$surf->write_to_png($OUTPUT);</syntaxhighlight>
Output: [https://raw.githubusercontent.com/SqrtNegInf/Rosettacode-Perl-Smoke/master/ref/b-spline.png b-spline.png] (offsite image)
=={{header|Phix}}==
{{trans|Wren}}
Line 51 ⟶ 478:
{{libheader|Phix/online}}
You can run this online [http://phix.x10.mx/p2js/bspline.htm here].
<!--<
<span style="color: #000080;font-style:italic;">--
-- demo\rosetta\B-spline.exw
Line 138 ⟶ 565:
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</
=={{header|Processing}}==
<syntaxhighlight lang="java">
//Aamrun, 26th June 2022
int abscissae[]={171,185,202,202,328,208,241,164,69,139,72,168};
int ordinates[] = {171,111,109,189 ,160,254 ,330 ,252,278 ,208 ,148 ,172};
void setup() {
size(450, 450);
background(255);
smooth();
noFill();
stroke(0);
beginShape();
for(int i=0;i<abscissae.length;i++){
curveVertex(abscissae[i], ordinates[i]);
}
endShape();
fill(255, 0, 0);
noStroke();
for (int i = 0; i < abscissae.length; i ++) {
ellipse(abscissae[i], ordinates[i], 3, 3);
}
}
</syntaxhighlight>
=={{header|Raku}}==
A minimal translation of [https://www.cypherpunk.at/download/bspline/bspline_1.1.tbz2 this C program], by [https://github.com/rahra Bernhard R. Fischer].
<syntaxhighlight lang="raku"
use Cairo;
Line 213 ⟶ 668:
};
.write_png(OUTPUT) and die # C return
}</
Output: [https://drive.google.com/file/d/1dInRJeecA18meybDF2D0usEaWMGFqoBj/view (Offsite image file) ]
=={{header|Wren}}==
{{libheader|DOME}}
Line 222 ⟶ 676:
If one uses a value for k of 1, then the script will simply plot the control points as in the Julia example.
<
import "graphics" for Canvas, Color
Line 283 ⟶ 737:
]
var k = 4 // polynomial degree is one less than this i.e. cubic
var Game = BSpline.new(400, 400, cpoints, k)</
| |||