function FlattenCSpline(const pts: TPathD): TPathD;
This function converts CSpline points into a flattened path. It loosely approximates the 'S' command inside the 'd' property of an SVG path. In essence, the 'pts' array represents a series of control points and coordinates that make up a series of joined cubic bezier curves.
The first four coordinates of the spline represent the starting point, two control points, and end point of the first sub-curve (just like a cubic bezier curve). Subsequent pairs of points represent the second control point and the end point for following sub-curves. Only two points are required for all but the first sub-curve because the end point of a preceding sub-curve becomes the starting point of the next sub-curve, and the second control point of a preceding sub-curve, once reflected across its end point, becomes the derived control point for the next sub-curve.
uses Image32, Image32_PNG, Image32_Vector, Image32_Draw; ... var img: TImage32; path: TPathD; pts: TPathD; ghostPt: TPointD; begin img := TImage32.Create(256,256); //CODE FOR (BLUE) QSPLINE OMITTED //create and draw a RED CSpine path pts := MakePathI([50,200, 40,160, 90,160, 80,200, 120,240, 110,200, 150,160, 140,200, 180,240, 170,200, 210,160, 200,200]); path := FlattenCSpline(pts); DrawLine(img, path, 8, clRed32, esRound); //show where the 'pts' are too for i := 0 to high(pts) do DrawPoint(img, pts[i], 3, clNavy32); //and show the derived control points i := 2; while i < high(pts) -1 do begin ghostPt := ReflectPoint(pts[i], pts[i +1]); DrawPoint(img, ghostPt, 3, clSilver32); inc(i, 2); end; img.SaveToFile('splines.png'); img.Free; end;
In the image below the red curve is a CSpine. The dark navy dots indicate the user defined control and end points, and the pale gray dots indicate virtual control points (ie derived from preceding control points).
Copyright ©2019 Angus Johnson - Image32 ver. 1.53 - Documentation last updated on 22-October-2020