public static Point2D QuadraticBezierEnvelope0(
Point2D point,
Rectangle2D bounds,
Point2D topLeft, Point2D topHandle, Point2D topRight, Point2D rightHandle,
Point2D bottomRight, Point2D bottomHandle, Point2D bottomLeft, Point2D leftHandle)
{
// topLeft topRight
// 0------------------0------------------0
// | topHandle |
// | |
// | |
// | |
// | |
// 0 leftHandle rightHandle 0
// | |
// | |
// | |
// | |
// | bottomHandle |
// 0------------------0------------------0
// bottomLeft bottomRight
//
// Install "Match Margin" Extension to enable word match highlighting, to help visualize where a variable resides in the ASCI map.
var normal = (X : (point.X - bounds.X) / bounds.Width, Y : (point.Y - bounds.Top) / bounds.Height);
var leftAnchor = InterpolateBezierQuadratic2DTests.QuadraticBezierInterpolate2D(normal.Y, topLeft.X, topLeft.Y, leftHandle.X, leftHandle.Y, bottomLeft.X, bottomLeft.Y);
var handle = InterpolateLinear2DTests.LinearInterpolate2D(normal.Y, topHandle.X, topHandle.Y, bottomHandle.X, bottomHandle.Y);
var rightAnchor = InterpolateBezierQuadratic2DTests.QuadraticBezierInterpolate2D(normal.Y, topRight.X, topRight.Y, rightHandle.X, rightHandle.Y, bottomRight.X, bottomRight.Y);
return(new Point2D(InterpolateBezierQuadratic2DTests.QuadraticBezierInterpolate2D(normal.X, leftAnchor.X, leftAnchor.Y, handle.X, handle.Y, rightAnchor.X, rightAnchor.Y)));
}
public static double QuadraticBezierArcLengthBySegments(
double ax, double ay,
double bx, double by,
double cx, double cy)
{
var length = 0d;
var p = InterpolateBezierQuadratic2DTests.QuadraticBezierInterpolate2D(0, ax, ay, bx, by, cx, cy);
var prevX = p.X;
var prevY = p.Y;
for (var t = 0.005; t <= 1.0; t += 0.005)
{
p = InterpolateBezierQuadratic2DTests.QuadraticBezierInterpolate2D(t, ay, ax, by, bx, cx, cy);
var deltaX = p.X - prevX;
var deltaY = p.Y - prevY;
length += Sqrt((deltaX * deltaX) + (deltaY * deltaY));
prevX = p.X;
prevY = p.Y;
}
// Exercise: due to roundoff, it's possible to miss a small segment at the end. how to compensate??
return(length);
}
public static (Point2D, double) FindNearestPoint(double aX, double aY, double bX, double bY, double cX, double cY, double x, double y)
{
var(a, b, c, d) = GetCubicPolynomialFromQuadraticBezierAndPointTests.GetCubicPolynomialFromQuadraticBezierAndPoint(aX, aY, bX, bY, cX, cY, x, y);
var candidates = FindAllRealRootsInIntervalTests.FindAllRootsInInterval(0d, 1d, a, b, c, d);
// Find the candidate that yields the closest point on the bezier to the given point.
var t = double.NaN;
var output = (double.NaN, double.NaN);
var minDistance = double.MaxValue;
foreach (var candidate in candidates)
{
var ptAtCandidate = InterpolateBezierQuadratic2DTests.QuadraticBezierInterpolate2D(candidate, aX, aY, bX, bY, cX, cY);
var distance = SquareDistanceTests.SquareDistance(ptAtCandidate.X, ptAtCandidate.Y, x, y);
if (distance < minDistance)
{
minDistance = distance;
t = candidate;
output = ptAtCandidate;
}
}
return(output, t);
}
public static Rectangle2D QuadraticBezierBounds0(
double ax, double ay,
double bx, double by,
double cx, double cy)
{
var sortOfCloseLength = QuadraticBezierSegmentLengthTests.QuadraticBezierArcLength(ax, ay, bx, by, cx, cy);
// ToDo: Need to make this more efficient. Don't need to rebuild the point array every time.
var points = new List <(double X, double Y)>(FunctionalInterpolationTests.Interpolate0to1((int)(sortOfCloseLength / 3), (i) => InterpolateBezierQuadratic2DTests.QuadraticBezierInterpolate2D(i, ax, ay, bx, by, cx, cy)));
var left = points[0].X;
var top = points[0].Y;
var right = points[0].X;
var bottom = points[0].Y;
foreach (var(X, Y) in points)
{
// ToDo: Measure performance impact of overwriting each time.
left = X <= left ? X : left;
top = Y <= top ? Y : top;
right = X >= right ? X : right;
bottom = Y >= bottom ? Y : bottom;
}
return(Rectangle2D.FromLTRB(left, top, right, bottom));
}