public static CubicBezier[] BuildCardinalSpline(Vector2[] pts, Vector2? m0, Vector2? mn, double tension) { if (pts.Length < 2) { throw new ArgumentException("There must be at least 2 points to construct cardinal spline", "pts"); } // compute reasonable starting and ending tangents if not supplied if (m0 == null) m0 = tension * (pts[1] - pts[0]); if (mn == null) mn = tension * (pts[pts.Length - 1] - pts[pts.Length - 2]); if (pts.Length == 2) { return new CubicBezier[] { CubicBezier.FromCubicHermite(pts[0], m0.Value, pts[1], mn.Value) }; } // we have > 2 points, so we will have n-1 beziers CubicBezier[] beziers = new CubicBezier[pts.Length - 1]; // fill in the first bezier beziers[0] = CubicBezier.FromCubicHermite(pts[0], m0.Value, pts[1], tension * (pts[2] - pts[0])); // iterate through and fill in all but the last for (int i = 1; i < pts.Length - 2; i++) { beziers[i] = CubicBezier.FromCubicHermite(pts[i], tension * (pts[i + 1] - pts[i - 1]), pts[i + 1], tension * (pts[i + 2] - pts[i])); } // fill int the last bezier beziers[pts.Length - 2] = CubicBezier.FromCubicHermite(pts[pts.Length - 2], tension * (pts[pts.Length - 1] - pts[pts.Length - 3]), pts[pts.Length - 1], mn.Value); // return the beziers return beziers; }
public static CubicBezier[] BuildC2Spline(Vector2[] pts, Vector2? m0, Vector2? mn, double tension) { if (pts.Length < 2) { throw new ArgumentException("There must be at least 2 points to construct cardinal spline", "pts"); } // compute reasonable starting and ending tangents if not supplied if (m0 == null) m0 = tension * (pts[1] - pts[0]); if (mn == null) mn = tension * (pts[pts.Length - 1] - pts[pts.Length - 2]); if (pts.Length == 2) { return new CubicBezier[] { CubicBezier.FromCubicHermite(pts[0], m0.Value, pts[1], mn.Value) }; } int n = pts.Length - 1; // we have > 2 points, so we will have n-1 beziers CubicBezier[] beziers = new CubicBezier[n]; // build up constraint matrix Matrix A = new Matrix(2 * n, 2 * n, 0); Matrix b = new Matrix(2 * n, 2); // matrix row index value int idx = 0; // add starting/ending tangent constraint Vector2 p01 = m0.Value / 3.0 + pts[0]; A[idx, 0] = 1; b[idx, 0] = p01.X; b[idx, 1] = p01.Y; idx++; Vector2 pn2 = -mn.Value / 3.0 + pts[n]; A[idx, 2 * n - 1] = 1; b[idx, 0] = pn2.X; b[idx, 1] = pn2.Y; idx++; // add C1 constraints for (int i = 0; i < n-1; i++) { A[idx, i * 2 + 1] = 1; A[idx, (i + 1) * 2] = 1; b[idx, 0] = pts[i + 1].X * 2; b[idx, 1] = pts[i + 1].Y * 2; idx++; } // add C2 constraints for (int i = 0; i < n-1; i++) { A[idx, i * 2] = 1; A[idx, i * 2 + 1] = -2; A[idx, (i + 1) * 2] = 2; A[idx, (i + 1) * 2 + 1] = -1; b[idx, 0] = 0; b[idx, 1] = 0; idx++; } // build the LUDecomposition of A to solve system A*P = b; LuDecomposition lu = new LuDecomposition(A); Matrix P = lu.Solve(b); // work back the Parameters for (int i = 0; i < n; i++) { beziers[i] = new CubicBezier(pts[i], new Vector2(P[2 * i, 0], P[2 * i, 1]), new Vector2(P[2 * i + 1, 0], P[2 * i + 1, 1]), pts[i + 1]); } return beziers; }
public static void DrawBezier(GLPen pen, Vector2 startP, Vector2 ctrl1, Vector2 ctrl2, Vector2 endP) { CubicBezier cb = new CubicBezier(startP, ctrl1, ctrl2, endP); pen.GLApplyPen(); Gl.glBegin(Gl.GL_LINE_STRIP); //iterate this bitch for (double i = 0; i < 1.0; i += .025) { Vector2 p = (cb.Bt(i)); Gl.glVertex2f((float)p.X, (float)p.Y); } Vector2 p1 = (cb.Bt(1)); Gl.glVertex2f((float)p1.X, (float)p1.Y); Gl.glEnd(); }
public BezierPathSegment(CubicBezier bezier, double? endSpeed, bool stopLine) { cb = bezier; this.endSpeed = endSpeed; this.stopLine = stopLine; }
public BezierPathSegment(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3, double? endSpeed, bool stopLine) { cb = new CubicBezier(p0, p1, p2, p3); this.endSpeed = endSpeed; this.stopLine = stopLine; }
public void Transform(Matrix3 m) { Vector3 p0 = new Vector3(cb.P0.X, cb.P0.Y, 1); Vector3 p1 = new Vector3(cb.P1.X, cb.P1.Y, 1); Vector3 p2 = new Vector3(cb.P2.X, cb.P2.Y, 1); Vector3 p3 = new Vector3(cb.P3.X, cb.P3.Y, 1); p0 = m * p0; p1 = m * p1; p2 = m * p2; p3 = m * p3; cb = new CubicBezier(new Vector2(p0.X, p0.Y), new Vector2(p1.X, p1.Y), new Vector2(p2.X, p2.Y), new Vector2(p3.X, p3.Y)); }