[rshapes] Add implementations
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Amy Wilder
GitHub
parent
cb3168a048
commit
51d849571d
408
src/rshapes.c
408
src/rshapes.c
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@ -2107,6 +2107,66 @@ void DrawSplineSegmentBezierCubic(Vector2 p1, Vector2 c2, Vector2 c3, Vector2 p4
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DrawTriangleStrip(points, 2*SPLINE_SEGMENT_DIVISIONS + 2, color);
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}
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// Draw spline segment with variable thickness: Cubic Bezier, 2 points, 2 control points, 1 or more thickness
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void DrawSplineSegmentBezierCubicVar(Vector2 p1, Vector2 c2, Vector2 c3, Vector2 p4, const float* thicks, int thickCount, Color color)
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{
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if (thickCount >= 1)
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{
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const float step = 1.0f/SPLINE_SEGMENT_DIVISIONS;
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Vector2 previous = p1;
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Vector2 current = { 0 };
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float t = 0.0f;
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Vector2 points[2*SPLINE_SEGMENT_DIVISIONS + 2] = { 0 };
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for (int i = 1; i <= SPLINE_SEGMENT_DIVISIONS; i++)
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{
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t = step*(float)i;
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float thick;
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if (thickCount > 1) {
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float tMajor = t*(float)thickCount;
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int tIndex = (int)tMajor;
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if (tIndex >= thickCount) tIndex = thickCount - 1;
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float tMinor = tMajor - (float)tIndex;
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thick = thicks[tIndex];
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} else {
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thick = thicks[0]; // constant thickness
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}
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float a = powf(1.0f - t, 3);
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float b = 3.0f*powf(1.0f - t, 2)*t;
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float c = 3.0f*(1.0f - t)*powf(t, 2);
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float d = powf(t, 3);
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current.y = a*p1.y + b*c2.y + c*c3.y + d*p4.y;
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current.x = a*p1.x + b*c2.x + c*c3.x + d*p4.x;
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float dy = current.y - previous.y;
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float dx = current.x - previous.x;
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float size = 0.5f*thick/sqrtf(dx*dx+dy*dy);
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if (i == 1)
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{
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points[0].x = previous.x + dy*size;
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points[0].y = previous.y - dx*size;
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points[1].x = previous.x - dy*size;
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points[1].y = previous.y + dx*size;
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}
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points[2*i + 1].x = current.x - dy*size;
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points[2*i + 1].y = current.y + dx*size;
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points[2*i].x = current.x + dy*size;
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points[2*i].y = current.y - dx*size;
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previous = current;
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}
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DrawTriangleStrip(points, 2*SPLINE_SEGMENT_DIVISIONS + 2, color);
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}
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}
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// Get spline point for a given t [0.0f .. 1.0f], Linear
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Vector2 GetSplinePointLinear(Vector2 startPos, Vector2 endPos, float t)
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{
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@ -2189,6 +2249,354 @@ Vector2 GetSplinePointBezierCubic(Vector2 startPos, Vector2 startControlPos, Vec
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return point;
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}
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// Get spline direction and speed, Linear Bezier
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//
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// Normalize to get the "forward" direction of the curve
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Vector2 GetSplineVelocityLinear(Vector2 startPos, Vector2 endPos)
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{
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Vector2 velocity = { 0 };
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velocity.x = endPos.x - startPos.x;
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velocity.y = endPos.y - startPos.y;
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return velocity;
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}
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// Get spline direction and speed for a given t [0.0f .. 1.0f], Quadratic Bezier
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//
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// Normalize to get the "forward" direction of the curve at t
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Vector2 GetSplineVelocityBezierQuad(Vector2 startPos, Vector2 controlPos, Vector2 endPos, float t)
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{
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Vector2 velocity = { 0 };
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float a = 2.0f*(1.0f - t);
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float b = 2.0f*t;
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velocity.x = a*(controlPos.x - startPos.x) + b*(endPos.x - controlPos.x);
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velocity.y = a*(controlPos.y - startPos.y) + b*(endPos.y - controlPos.y);
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return velocity;
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}
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// Get spline direction and speed for a given t [0.0f .. 1.0f], Cubic Bezier
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//
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// Normalize to get the "forward" direction of the curve at t
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Vector2 GetSplineVelocityBezierCubic(Vector2 startPos, Vector2 startControlPos, Vector2 endControlPos, Vector2 endPos, float t)
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{
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Vector2 velocity = { 0 };
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float a = 3.0f*powf(1.0f - t, 2);
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float b = 6.0f*(1.0f - t)*t;
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float c = 3.0f*t*t;
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velocity.x = a*(startControlPos.x - startPos.x) + b*(endControlPos.x - startControlPos.x) + c*(endPos.x - endControlPos.x);
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velocity.y = a*(startControlPos.y - startPos.y) + b*(endControlPos.y - startControlPos.y) + c*(endPos.y - endControlPos.y);
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return velocity;
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}
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// Get spline rate of change, Quadratic Bezier
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Vector2 GetSplineAccelerationBezierQuad(Vector2 startPos, Vector2 controlPos, Vector2 endPos)
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{
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Vector2 acceleration = { 0 };
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acceleration.x = 2.0f*(endPos.x - 2.0f*controlPos.x - startPos.x);
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acceleration.y = 2.0f*(endPos.y - 2.0f*controlPos.y - startPos.y);
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return acceleration;
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}
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// Get spline rate of change for a given t [0.0f .. 1.0f], Cubic Bezier
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Vector2 GetSplineAccelerationBezierCubic(Vector2 startPos, Vector2 startControlPos, Vector2 endControlPos, Vector2 endPos, float t)
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{
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Vector2 acceleration = { 0 };
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float a = 2.0f*(1.0f - t);
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float b = 2.0f*t;
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acceleration.x = a*(endControlPos.x - 2.0f*startControlPos.x + startPos.x) + b*(endPos.x - 2.0f*endControlPos.x + startControlPos.x);
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acceleration.y = a*(endControlPos.y - 2.0f*startControlPos.y + startPos.y) + b*(endPos.y - 2.0f*endControlPos.y + startControlPos.y);
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return acceleration;
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}
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// Get spline rate of acceleration, Cubic Bezier
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Vector2 GetSplineJoltBezierCubic(Vector2 startPos, Vector2 startControlPos, Vector2 endControlPos, Vector2 endPos)
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{
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Vector2 jolt = { 0 };
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jolt.x = 6.0f*(endPos.x + 3.0f*(startControlPos.x - endControlPos.x) - startPos.x);
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jolt.y = 6.0f*(endPos.y + 3.0f*(startControlPos.y - endControlPos.y) - startPos.y);
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return jolt;
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}
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// Compute spline curve bounding rectangle, Linear Bezier
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Rectangle GetSplineBoundsBezierLinear(Vector2 startPos, Vector2 endPos)
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{
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float xMin;
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float yMin;
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float xMax;
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float yMax;
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if (startPos.x < endPos.x)
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{
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xMin = startPos.x;
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xMax = endPos.x;
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}
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else
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{
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xMin = endPos.x;
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xMax = startPos.x;
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}
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if (startPos.y < endPos.y)
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{
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yMin = startPos.y;
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yMax = endPos.y;
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}
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else
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{
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yMin = endPos.y;
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yMax = startPos.y;
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}
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// straight line will never escape bounds
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Rectangle bounds = { xMin, yMin, xMax - xMin, yMax - yMin };
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return bounds;
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}
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// Compute spline curve bounding rectangle, Quadratic Bezier
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Rectangle GetSplineBoundsBezierQuad(Vector2 startPos, Vector2 controlPos, Vector2 endPos)
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{
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float xMin;
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float yMin;
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float xMax;
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float yMax;
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if (startPos.x < endPos.x)
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{
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xMin = startPos.x;
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xMax = endPos.x;
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}
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else
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{
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xMin = endPos.x;
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xMax = startPos.x;
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}
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if (startPos.y < endPos.y)
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{
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yMin = startPos.y;
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yMax = endPos.y;
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}
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else
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{
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yMin = endPos.y;
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yMax = startPos.y;
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}
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// curve velocity, rearranged to solve for t
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// at^2 + bt + c
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// local min/max occur where derivative (velocity) is zero,
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// so we use quadratic formula to find values of t at zeros
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float a = startPos.x - 2.0f*controlPos.x + endPos.x;
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float b = 2.0f*(controlPos.x - startPos.x);
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float c = startPos.x;
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bool dejavu = false;
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do
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{
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if (a != 0)
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{
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float bSqrMinus4ac = b*b - 4.0f*a*c;
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float t[2] = { 0 };
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int tCount = 0;
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if (bSqrMinus4ac > 0)
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{
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float denominator = 1.0f/(2.0f*a);
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float term0 = -b*denominator;
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float term1 = sqrtf(bSqrMinus4ac)*denominator;
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t[0] = term0 + term1;
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if (0.0f < t[0] && t[0] < 1.0f) ++tCount;
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t[tCount] = term0 - term1;
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if (0.0f < t[tCount] && t[tCount] < 1.0f) ++tCount;
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}
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else if (bSqrMinus4ac == 0)
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{
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t[0] = -b/(2.0f*a);
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if (0.0f < t[0] && t[0] < 1.0f) ++tCount;
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}
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// ignore imaginary solution
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for (int i = 0; i < tCount; ++i)
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{
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Vector2 point = GetSplinePointBezierQuad(startPos, controlPos, endPos, t[i]);
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if (point.x < xMin) xMin = point.x;
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if (point.x > xMax) xMax = point.x;
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if (point.y < yMin) yMin = point.y;
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if (point.y > yMax) yMax = point.y;
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}
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}
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// straight line will never escape bounds
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if (dejavu) break;
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dejavu = true;
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a = startPos.y - 2.0f*controlPos.y + endPos.y;
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b = 2.0f*(controlPos.y - startPos.y);
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c = startPos.y;
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}
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while (true);
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Rectangle bounds = { xMin, yMin, xMax - xMin, yMax - yMin };
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return bounds;
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}
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// Compute spline curve bounding rectangle, Cubic Bezier
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Rectangle GetSplineBoundsBezierCubic(Vector2 startPos, Vector2 startControlPos, Vector2 endControlPos, Vector2 endPos)
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{
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float xMin;
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float yMin;
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float xMax;
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float yMax;
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if (startPos.x < endPos.x)
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{
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xMin = startPos.x;
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xMax = endPos.x;
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}
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else
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{
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xMin = endPos.x;
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xMax = startPos.x;
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}
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if (startPos.y < endPos.y)
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{
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yMin = startPos.y;
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yMax = endPos.y;
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}
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else
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{
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yMin = endPos.y;
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yMax = startPos.y;
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}
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// curve velocity, rearranged to solve for t
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// at^2 + bt + c
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// local min/max occur where derivative (velocity) is zero,
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// so we use quadratic formula to find values of t at zeros
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float a = -3.0f*startPos.x + 9.0f*startControlPos.x - 9.0f*endControlPos.x + 3.0f*endPos.x;
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float b = 6.0f*startPos.x - 12.0f*startControlPos.x + 6.0f*endControlPos.x;
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float c = -3.0f*startPos.x + 3.0f*startControlPos.x;
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bool dejavu = false;
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do
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{
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if (a != 0)
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{
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float bSqrMinus4ac = b*b - 4.0f*a*c;
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float t[2] = { 0 };
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int tCount = 0;
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if (bSqrMinus4ac > 0)
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{
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float denominator = 1.0f/(2.0f*a);
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float term0 = -b*denominator;
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float term1 = sqrtf(bSqrMinus4ac)*denominator;
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t[0] = term0 + term1;
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if (0.0f < t[0] && t[0] < 1.0f) ++tCount;
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t[tCount] = term0 - term1;
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if (0.0f < t[tCount] && t[tCount] < 1.0f) ++tCount;
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}
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else if (bSqrMinus4ac == 0)
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{
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t[0] = -b/(2.0f*a);
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if (0.0f < t[0] && t[0] < 1.0f) ++tCount;
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}
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// ignore imaginary solution
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for (int i = 0; i < tCount; ++i)
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{
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Vector2 point = GetSplinePointBezierCubic(startPos, startControlPos, endControlPos, endPos, t[i]);
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if (point.x < xMin) xMin = point.x;
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if (point.x > xMax) xMax = point.x;
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if (point.y < yMin) yMin = point.y;
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if (point.y > yMax) yMax = point.y;
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}
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}
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// straight line will never escape bounds
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if (dejavu) break;
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dejavu = true;
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a = -3.0f*startPos.x + 9.0f*startControlPos.x - 9.0f*endControlPos.x + 3.0f*endPos.x;
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b = 6.0f*startPos.x - 12.0f*startControlPos.x + 6.0f*endControlPos.x;
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c = -3.0f*startPos.x + 3.0f*startControlPos.x;
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}
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while (true);
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Rectangle bounds = { xMin, yMin, xMax - xMin, yMax - yMin };
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return bounds;
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}
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// Reciprocal radius (or "radians per meter") for a given t [0.0f .. 1.0f], Cubic Bezier
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float GetSplineCurvatureBezierCubic(Vector2 startPos, Vector2 startControlPos, Vector2 endControlPos, Vector2 endPos, float t)
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{
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float curvature = 0.0f;
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float a = 3.0f*powf(1.0f - t, 2);
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float b = 6.0f*(1.0f - t)*t;
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float c = 3.0f*t*t;
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Vector2 velocity = { 0 };
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velocity.x = a*(startControlPos.x - startPos.x) + b*(endControlPos.x - startControlPos.x) + c*(endPos.x - endControlPos.x);
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velocity.y = a*(startControlPos.y - startPos.y) + b*(endControlPos.y - startControlPos.y) + c*(endPos.y - endControlPos.y);
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a = 2.0f*(1.0f - t);
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b = 2.0f*t;
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Vector2 acceleration = { 0 };
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acceleration.x = a*(endControlPos.x - 2.0f*startControlPos.x + startPos.x) + b*(endPos.x - 2.0f*endControlPos.x + startControlPos.x);
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acceleration.y = a*(endControlPos.y - 2.0f*startControlPos.y + startPos.y) + b*(endPos.y - 2.0f*endControlPos.y + startControlPos.y);
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float curvature = (velocity.x*acceleration.y - velocity.y*acceleration.x)/powf(sqrtf(velocity.x*velocity.x + velocity.y*velocity.y), 3);
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return curvature;
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}
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// Get value of t (unbounded) for the point on the line closest to a given position
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float GetSplineNearestTLinear(Vector2 startPos, Vector2 endPos, Vector2 point)
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{
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Vector2 edge = { 0 };
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edge.x = endPos.x - startPos.x;
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edge.y = endPos.y - startPos.y;
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Vector2 diff = { 0 };
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diff.x = point.x - startPos.x;
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diff.y = point.y - startPos.y;
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float t = (edge.x*diff.x + edge.y*diff.y)/(edge.x*edge.x + edge.y*edge.y);
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return t;
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}
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//----------------------------------------------------------------------------------
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// Module Functions Definition - Collision Detection functions
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//----------------------------------------------------------------------------------
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