Bitmap/Bézier curves/Quadratic: Difference between revisions
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See [[Cubic bezier curves#J|Cubic bezier curves]] for a generalized solution.
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<lang Mathematica>pts = {{0, 0}, {1, -1}, {2, 1}};
Graphics[{BSplineCurve[pts], Green, Line[pts], Red, Point[pts]}]</lang>
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Revision as of 19:50, 16 October 2015
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).
Ada
<lang ada>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;</lang> The following test <lang ada> X : Image (1..16, 1..16); begin
Fill (X, White); Quadratic_Bezier (X, (8, 2), (13, 8), (2, 15), Black); Print (X);</lang>
should produce;
H H H H H HH HH H HH HHH HH
BBC BASIC
<lang bbcbasic> 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</lang>
C
Interface (to be added to all other to make the final imglib.h):
<lang c>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 );</lang>
Implementation:
<lang c>#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</lang>
D
This solution uses two modules, from the Grayscale image and the Bresenham's line algorithm Tasks. <lang d>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();
}</lang>
- 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: <lang qbasic>#DEFINE WM_LBUTTONDOWN 513
- DEFINE WM_CLOSE 16
FBSLSETTEXT(ME, "Bezier Quadratic") FBSLSETFORMCOLOR(ME, RGB(0, 255, 255)) ' Cyan: persistent background color DRAWWIDTH(5) ' Adjust point size FBSL.GETDC(ME) ' Use volatile FBSL.GETDC below to avoid extra assignments
RESIZE(ME, 0, 0, 235, 235) CENTER(ME) SHOW(ME)
DIM Height AS INTEGER FBSL.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 SELECT END 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 SUB END SUB</lang> 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 <lang factor>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 ;
</lang>
Fortran
(This subroutine must be inside the RCImagePrimitive
module, see here)
<lang fortran>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</lang>
Go
<lang go>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())
}</lang> Demonstration program:
<lang go>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) }
}</lang>
Haskell
<lang haskell>{-# LANGUAGE
FlexibleInstances, TypeSynonymInstances, ViewPatterns #-}
import Bitmap import Bitmap.Line import Control.Monad import 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 -> Point pmap f (x, y) = (f x, f y)
onCoordinates :: (Double -> Double -> Double) -> Point -> Point -> Point onCoordinates 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</lang>
J
See Cubic bezier curves for a generalized solution.
Mathematica / Wolfram Language
<lang Mathematica>pts = {{0, 0}, {1, -1}, {2, 1}}; Graphics[{BSplineCurve[pts], Green, Line[pts], Red, Point[pts]}]</lang>
MATLAB
Note: Store this function in a file named "bezierQuad.mat" in the @Bitmap folder for the Bitmap class defined here. <lang MATLAB> 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 </lang>
Sample usage: This will generate the image example for the Go solution. <lang MATLAB> >> img = Bitmap(400,300); >> img.fill([223 255 239]); >> img.bezierQuad([20 150],[500 -100],[300 280],[63 143 239],21); >> disp(img) </lang>
OCaml
<lang 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);
- </lang>
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 <lang Phix>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, c sequence 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 img
end 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)</lang>
PicoLisp
This uses the 'brez' line drawing function from Bitmap/Bresenham's line algorithm#PicoLisp. <lang 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) ) ) ) )</lang>
Test: <lang PicoLisp>(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")</lang>
PureBasic
<lang 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, img w = 200: h = 200: img = 1 CreateImage(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 event Repeat
event = WaitWindowEvent()
Until event = #PB_Event_CloseWindow </lang>
Python
See Cubic bezier curves#Python for a generalized solution.
R
See Cubic bezier curves#R for a generalized solution.
Racket
<lang 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 </lang>
Ruby
See Cubic bezier curves#Ruby for a generalized solution.
Tcl
See Cubic bezier curves#Tcl for a generalized solution.
TI-89 BASIC
<lang ti89b>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 EndFor
EndPrgm</lang>
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.
<lang vedit>// 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</lang>
XPL0
<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations
proc Bezier(P0, P1, P2); \Draw quadratic Bezier curve real 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 points Point(fix(P1(0)), fix(P1(1)), $FF0000); Point(fix(P2(0)), fix(P2(1)), $FF0000); ];
[SetVid($112); \set 640x480x24 video graphics Bezier([0., 0.], [80., 100.], [160., 20.]); if ChIn(1) then []; \wait for keystroke SetVid(3); \restore normal text display ]</lang>
zkl
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
Add this to the PPM class: <lang zkl> 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);
}); }</lang>
Doesn't use line segments, they don't seem like an improvement. <lang zkl>bitmap:=PPM(200,200,0xff|ff|ff); bitmap.qBezier(10,100, 250,270, 150,20, 0); bitmap.write(File("foo.ppm","wb"));</lang>
- Output: