public static void general_intersections()
{
var line = new Line2(new Point2(2, 1), new Vector2(2, 1));
line.Intersects(new Point2(-2, -1)).Should().BeTrue();
line.Intersects(new Point2(0, 0)).Should().BeTrue();
line.Intersects(new Point2(1, 0.5)).Should().BeTrue();
line.Intersects(new Point2(2, 1)).Should().BeTrue();
line.Intersects(new Point2(4, 2)).Should().BeTrue();
line.Intersects(new Point2(1, 2)).Should().BeFalse();
}
public static void line_ray_basic_intersection_testing()
{
var a = new Line2(new Point2(3, 3), new Vector2(1, 1));
var b = new Ray2(new Point2(0, 1), new Vector2(0, 1));
var c = new Ray2(new Point2(2, 2), new Vector2(-1, -1));
var d = new Ray2(new Point2(2, 3), new Vector2(-1, -1));
a.Intersects(b.GetReverse()).Should().BeTrue();
a.Intersects(c).Should().BeTrue();
a.Intersects(c.GetReverse()).Should().BeTrue();
a.Intersects(b).Should().BeFalse();
a.Intersects(d).Should().BeFalse();
a.Intersects(d.GetReverse()).Should().BeFalse();
}
public static void line_line_basic_intersection_testing()
{
var a = new Line2(new Point2(3, 3), new Vector2(1, 1));
var b = new Line2(new Point2(0, 1), new Vector2(0, 1));
var c = new Line2(new Point2(2, 2), new Vector2(-1, -1));
var d = new Line2(new Point2(2, 3), new Vector2(-1, -1));
var e = new Line2(new Point2(2, 3), new Vector2(-2, -2));
var f = new Line2(new Point2(2, 3), new Vector2(0.5, 0.5));
a.Intersects(a).Should().BeTrue();
a.Intersects(b).Should().BeTrue();
a.Intersects(c).Should().BeTrue();
a.Intersects(d).Should().BeFalse();
a.Intersects(e).Should().BeFalse();
a.Intersects(f).Should().BeFalse();
}
private Circle2 FitCirleToThreePoints(IVector2 p1, IVector2 p2, IVector2 p3)
{
try
{
double x1 = (p1.X + p2.X) / 2.0;
double y1 = (p1.Y + p2.Y) / 2.0;
double dy1 = p2.X - p1.X;
double dx1 = -1 * (p2.Y - p1.Y);
double x2 = (p3.X + p2.X) / 2.0;
double y2 = (p3.Y + p2.Y) / 2.0;
double dy2 = p3.X - p2.X;
double dx2 = -1 * (p3.Y - p2.Y);
var line1 = new Line2(new Vector2(x1, y1), new Vector2(x1 + dx1, y1 + dy1));
var line2 = new Line2(new Vector2(x2, y2), new Vector2(x2 + dx2, y2 + dy2));
var intersection = line1.Intersects(line2);
if (!(intersection.Intersects))
{
throw new Exception("Points are colinear, Couldn't find arc");
}
else
{
var center = new Vector2(intersection.Point.X, intersection.Point.Y);
var dx = center.X - p1.X;
var dy = center.Y - p1.Y;
var r = Math.Sqrt(dx * dx + dy * dy);
if (double.IsNaN(center.X) || double.IsNaN(center.Y) || double.IsNaN(r))
{
throw new ArgumentException("Unable to calculate center or radius of fitting circle");
}
return(new Circle2(center, r));
}
}
catch (Exception)
{
throw;
}
}
/// <summary>
/// Draws the area between two curves using the provided color.
/// </summary>
/// <param name="curves">Curves to draw within the currently set range.</param>
/// <param name="color">Color to draw the area with.</param>
private void DrawCurveRange(EdAnimationCurve[] curves, Color color)
{
float range = GetRange(true);
if (curves.Length != 2 || curves[0] == null || curves[1] == null)
{
return;
}
KeyFrame[][] keyframes = { curves[0].KeyFrames, curves[1].KeyFrames };
if (keyframes[0].Length <= 0 || keyframes[1].Length <= 0)
{
return;
}
int numSamples = (drawableWidth + LINE_SPLIT_WIDTH - 1) / LINE_SPLIT_WIDTH;
float timePerSample = range / numSamples;
float time = rangeOffset;
float lengthPerPixel = rangeLength / drawableWidth;
time -= lengthPerPixel * PADDING;
int[] keyframeIndices = { 0, 0 };
// Find first valid keyframe indices
for (int curveIdx = 0; curveIdx < 2; curveIdx++)
{
keyframeIndices[curveIdx] = keyframes[curveIdx].Length;
for (int i = 0; i < keyframes[curveIdx].Length; i++)
{
if (keyframes[curveIdx][i].time > time)
{
keyframeIndices[curveIdx] = i;
}
}
}
List <float> times = new List <float>();
List <float>[] points = { new List <float>(), new List <float>() };
// Determine start points
for (int curveIdx = 0; curveIdx < 2; curveIdx++)
{
float value = curves[curveIdx].Evaluate(time, false);
points[curveIdx].Add(value);
}
times.Add(time);
float rangeEnd = rangeOffset + range;
while (time < rangeEnd)
{
float nextTime = time + timePerSample;
bool hasStep = false;
// Determine time to sample at. Use fixed increments unless there's a step keyframe within our increment in
// which case we use its time so we can evaluate it directly
for (int curveIdx = 0; curveIdx < 2; curveIdx++)
{
int keyframeIdx = keyframeIndices[curveIdx];
if (keyframeIdx < keyframes[curveIdx].Length)
{
KeyFrame keyframe = keyframes[curveIdx][keyframeIdx];
bool isStep = keyframe.inTangent == float.PositiveInfinity ||
keyframe.outTangent == float.PositiveInfinity;
if (isStep && keyframe.time <= nextTime)
{
nextTime = Math.Min(nextTime, keyframe.time);
hasStep = true;
}
}
}
// Evaluate
if (hasStep)
{
for (int curveIdx = 0; curveIdx < 2; curveIdx++)
{
int keyframeIdx = keyframeIndices[curveIdx];
if (keyframeIdx < keyframes[curveIdx].Length)
{
KeyFrame keyframe = keyframes[curveIdx][keyframeIdx];
if (MathEx.ApproxEquals(keyframe.time, nextTime))
{
if (keyframeIdx > 0)
{
KeyFrame prevKeyframe = keyframes[curveIdx][keyframeIdx - 1];
points[curveIdx].Add(prevKeyframe.value);
}
else
{
points[curveIdx].Add(keyframe.value);
}
points[curveIdx].Add(keyframe.value);
}
else
{
// The other curve has step but this one doesn't, we just insert the same value twice
float value = curves[curveIdx].Evaluate(nextTime, false);
points[curveIdx].Add(value);
points[curveIdx].Add(value);
}
times.Add(nextTime);
times.Add(nextTime);
}
}
}
else
{
for (int curveIdx = 0; curveIdx < 2; curveIdx++)
{
points[curveIdx].Add(curves[curveIdx].Evaluate(nextTime, false));
}
times.Add(nextTime);
}
// Advance keyframe indices
for (int curveIdx = 0; curveIdx < 2; curveIdx++)
{
int keyframeIdx = keyframeIndices[curveIdx];
while (keyframeIdx < keyframes[curveIdx].Length)
{
KeyFrame keyframe = keyframes[curveIdx][keyframeIdx];
if (keyframe.time > nextTime)
{
break;
}
keyframeIdx = ++keyframeIndices[curveIdx];
}
}
time = nextTime;
}
// End points
for (int curveIdx = 0; curveIdx < 2; curveIdx++)
{
float value = curves[curveIdx].Evaluate(rangeEnd, false);
points[curveIdx].Add(value);
}
times.Add(rangeEnd);
int numQuads = times.Count - 1;
List <Vector2I> vertices = new List <Vector2I>();
for (int i = 0; i < numQuads; i++)
{
int idxLeft = points[0][i] < points[1][i] ? 0 : 1;
int idxRight = points[0][i + 1] < points[1][i + 1] ? 0 : 1;
Vector2[] left =
{
new Vector2(times[i], points[0][i]),
new Vector2(times[i], points[1][i])
};
Vector2[] right =
{
new Vector2(times[i + 1], points[0][i + 1]),
new Vector2(times[i + 1], points[1][i + 1])
};
if (idxLeft == idxRight)
{
int idxA = idxLeft;
int idxB = (idxLeft + 1) % 2;
vertices.Add(CurveToPixelSpace(left[idxB]));
vertices.Add(CurveToPixelSpace(right[idxB]));
vertices.Add(CurveToPixelSpace(left[idxA]));
vertices.Add(CurveToPixelSpace(right[idxB]));
vertices.Add(CurveToPixelSpace(right[idxA]));
vertices.Add(CurveToPixelSpace(left[idxA]));
}
// Lines intersects, can't represent them with a single quad
else if (idxLeft != idxRight)
{
int idxA = idxLeft;
int idxB = (idxLeft + 1) % 2;
Line2 lineA = new Line2(left[idxB], right[idxA] - left[idxB]);
Line2 lineB = new Line2(left[idxA], right[idxB] - left[idxA]);
if (lineA.Intersects(lineB, out var t))
{
Vector2 intersection = left[idxB] + t * (right[idxA] - left[idxB]);
vertices.Add(CurveToPixelSpace(left[idxB]));
vertices.Add(CurveToPixelSpace(intersection));
vertices.Add(CurveToPixelSpace(left[idxA]));
vertices.Add(CurveToPixelSpace(intersection));
vertices.Add(CurveToPixelSpace(right[idxB]));
vertices.Add(CurveToPixelSpace(right[idxA]));
}
}
}
canvas.DrawTriangleList(vertices.ToArray(), color, 129);
}
private static List <Triangle> Cut(Triangle tri, Line3 line)
{
// Create coordinate system
Vec3 norm = tri.Normal;
Vec3 xaxis = tri.Edge13.Normalized;
Vec3 yaxis = Vec3.Cross(norm, xaxis);
// Convert to 2d space
Vec2 v1 = Vec2.Zero; // Consider point 0 the origin
Vec2 v2 = Collapse(tri.Item2 - tri.Item1, xaxis, yaxis); // Relative position of Item2
Vec2 v3 = Collapse(tri.Item3 - tri.Item1, xaxis, yaxis); // Relative position of Item3
Vec2 ls = Collapse(line.Item1 - tri.Item1, xaxis, yaxis);
Vec2 le = Collapse(line.Item2 - tri.Item1, xaxis, yaxis);
Line2 l12 = new Line2(v1, v2);
Line2 l13 = new Line2(v1, v3);
Line2 l23 = new Line2(v2, v3);
Line2 cut = new Line2(ls, le);
// Perform intersection test
double k12, k13, k23;
double c12, c13, c23;
bool i12 = l12.Intersects(cut, out c12, out k12);
bool i13 = l13.Intersects(cut, out c13, out k13);
bool i23 = l23.Intersects(cut, out c23, out k23);
// Check cases
List <Triangle> tris = new List <Triangle>();
// Corner - Edge intersection (3 cases)
if (IsCorner(c12, c13) && IsEdge(c23))
{
// Crossing from corner 1 to edge 2->3
Vec3 midpoint = Vec3.Lerp(tri.Item2, tri.Item3, c23);
tris.Add(new Triangle(tri.Item1, tri.Item2, midpoint));
tris.Add(new Triangle(tri.Item1, midpoint, tri.Item3));
return(tris);
}
else if (IsCorner(c13, c23) && IsEdge(c12))
{
// Crossing from corner 3 to edge 1->2
Vec3 midpoint = Vec3.Lerp(tri.Item1, tri.Item2, c12);
tris.Add(new Triangle(tri.Item1, midpoint, tri.Item3));
tris.Add(new Triangle(midpoint, tri.Item2, tri.Item3));
return(tris);
}
else if (IsCorner(c12, c23) && IsEdge(c13))
{
// Crossing from corner 2 to edge 1->3
Vec3 midpoint = Vec3.Lerp(tri.Item1, tri.Item3, c13);
tris.Add(new Triangle(tri.Item1, tri.Item2, midpoint));
tris.Add(new Triangle(midpoint, tri.Item2, tri.Item3));
return(tris);
}
// Edge - Edge intersection (3 cases)
else if (IsEdge(c12) && IsEdge(c23))
{
// Collision crossing 1->2, 2->3
Vec3 m1 = Vec3.Lerp(tri.Item1, tri.Item2, c12);
Vec3 m2 = Vec3.Lerp(tri.Item2, tri.Item3, c23);
Vec3 mid = (tri.Item1 + tri.Item3) / 2;
tris.Add(new Triangle(tri.Item1, m1, mid));
tris.Add(new Triangle(m1, m2, mid));
tris.Add(new Triangle(mid, m2, tri.Item3));
tris.Add(new Triangle(m1, tri.Item2, m2));
return(tris);
}
else if (IsEdge(c12) && IsEdge(c13))
{
// Collision crossing 1->3, 1->2
Vec3 m1 = Vec3.Lerp(tri.Item1, tri.Item2, c12);
Vec3 m2 = Vec3.Lerp(tri.Item1, tri.Item3, c13);
Vec3 mid = (tri.Item2 + tri.Item3) / 2;
tris.Add(new Triangle(m1, tri.Item2, mid));
tris.Add(new Triangle(m1, mid, m2));
tris.Add(new Triangle(m2, mid, tri.Item3));
tris.Add(new Triangle(tri.Item1, m1, m2));
return(tris);
}
else if (IsEdge(c13) && IsEdge(c23))
{
// Collision crossing 1->3, 2->3
Vec3 m1 = Vec3.Lerp(tri.Item1, tri.Item3, c13);
Vec3 m2 = Vec3.Lerp(tri.Item2, tri.Item3, c23);
Vec3 mid = (tri.Item1 + tri.Item2) / 2;
tris.Add(new Triangle(mid, tri.Item2, m2));
tris.Add(new Triangle(mid, m2, m1));
tris.Add(new Triangle(tri.Item1, mid, m1));
tris.Add(new Triangle(m1, m2, tri.Item3));
return(tris);
}
// No intersection (1 case)
else
{
tris.Add(tri);
return(tris);
}
}
public static void general_intersections() {
var line = new Line2(new Point2(2, 1), new Vector2(2, 1));
line.Intersects(new Point2(-2, -1)).Should().BeTrue();
line.Intersects(new Point2(0, 0)).Should().BeTrue();
line.Intersects(new Point2(1, 0.5)).Should().BeTrue();
line.Intersects(new Point2(2, 1)).Should().BeTrue();
line.Intersects(new Point2(4, 2)).Should().BeTrue();
line.Intersects(new Point2(1, 2)).Should().BeFalse();
}
public static void line_ray_basic_intersection_testing() {
var a = new Line2(new Point2(3, 3), new Vector2(1, 1));
var b = new Ray2(new Point2(0, 1), new Vector2(0, 1));
var c = new Ray2(new Point2(2, 2), new Vector2(-1, -1));
var d = new Ray2(new Point2(2, 3), new Vector2(-1, -1));
a.Intersects(b.GetReverse()).Should().BeTrue();
a.Intersects(c).Should().BeTrue();
a.Intersects(c.GetReverse()).Should().BeTrue();
a.Intersects(b).Should().BeFalse();
a.Intersects(d).Should().BeFalse();
a.Intersects(d.GetReverse()).Should().BeFalse();
}
public static void line_line_basic_intersection_testing() {
var a = new Line2(new Point2(3, 3), new Vector2(1, 1));
var b = new Line2(new Point2(0, 1), new Vector2(0, 1));
var c = new Line2(new Point2(2, 2), new Vector2(-1, -1));
var d = new Line2(new Point2(2, 3), new Vector2(-1, -1));
var e = new Line2(new Point2(2, 3), new Vector2(-2, -2));
var f = new Line2(new Point2(2, 3), new Vector2(0.5, 0.5));
a.Intersects(a).Should().BeTrue();
a.Intersects(b).Should().BeTrue();
a.Intersects(c).Should().BeTrue();
a.Intersects(d).Should().BeFalse();
a.Intersects(e).Should().BeFalse();
a.Intersects(f).Should().BeFalse();
}