RNClassID R3Span::
Clip(const R3Plane& plane)
{
// Characterize endpoints with respect to plane
RNScalar d1 = R3SignedDistance(plane, Start());
RNScalar d2 = R3SignedDistance(plane, End());
// Clip span to plane
if (RNIsNegative(d1)) {
if (RNIsNegative(d2)) {
// Both points are below plane ???
Reset(Start(), Start());
return RN_NULL_CLASS_ID;
}
else if (RNIsPositive(d2)) {
// Start is below, end is above -- move start to plane
Reset((Start() * d2 + End() * -d1) / (d2 - d1), End());
return R3_SPAN_CLASS_ID;
}
else {
// Start is below, end is on -- move start to end
Reset(End(), End());
return R3_POINT_CLASS_ID;
}
}
else if (RNIsPositive(d1)) {
if (RNIsNegative(d2)) {
// Start is above, end is below -- move end to plane
Reset(Start(), (Start() * -d2 + End() * d1) / (d1 - d2));
return R3_SPAN_CLASS_ID;
}
else {
// Start is above, end is on or above
return R3_SPAN_CLASS_ID;
}
}
else {
if (RNIsNegative(d2)) {
// Start is on, end is below -- move end to start
Reset(Start(), Start());
return R3_POINT_CLASS_ID;
}
else {
// Start is on, end is on or above
return R3_SPAN_CLASS_ID;
}
}
}
RNLength R2Distance(const R2Point& point, const R2Halfspace& halfspace)
{
// Return distance from point to halfspace
RNScalar d = R2SignedDistance(halfspace.Line(), point);
if (RNIsNegative(d)) return -d;
else return 0.0;
}
RNLength R2Distance(const R2Span& span, const R2Halfspace& halfspace)
{
// Return distance from span to halfspace
RNScalar d = R2SignedDistance(halfspace.Line(), span);
if (RNIsNegative(d)) return -d;
else return 0.0;
}
RNLength R2Distance(const R2Ray& ray, const R2Halfspace& halfspace)
{
// Return distance from ray to halfspace
RNScalar d = R2SignedDistance(halfspace.Line(), ray);
if (RNIsNegative(d)) return -d;
else return 0.0;
}
const RNBoolean R3Matrix::
HasMirror(void) const
{
// Return whether matrix transformation has mirror operator
R2Vector vx(m[0][0], m[1][0]);
R2Vector vy(m[0][1], m[1][1]);
return RNIsNegative(vx % vy);
}
RNLength R2Distance(const R2Line& line, const R2Span& span)
{
// Return distance from span to line
RNScalar d = R2SignedDistance(line, span);
if (RNIsPositive(d)) return d;
else if (RNIsNegative(d)) return -d;
else return 0.0;
}
const RNBoolean R4Matrix::
HasMirror(void) const
{
// Return whether matrix transformation has mirror operator
R3Vector vx(m[0][0], m[1][0], m[2][0]);
R3Vector vy(m[0][1], m[1][1], m[2][1]);
R3Vector vz(m[0][2], m[1][2], m[2][2]);
return RNIsNegative(vz.Dot(vx % vy));
}
RNLength R2Distance(const R2Point& point, const R2Ray& ray)
{
// Check if start point is closest
R2Vector v = point - ray.Start();
RNScalar dir = v.Dot(ray.Vector());
if (RNIsNegative(dir)) return v.Length();
// Return distance from point to ray line
return R2Distance(point, ray.Line());
}
RNLength R2SignedDistance(const R2Line& line, const R2Box& box)
{
// Return signed distance from line to box
RNQuadrant quadrant = line.Normal().Quadrant();
RNScalar d1 = R2SignedDistance(line, box.Corner(~quadrant & 0x3));
if (RNIsPositiveOrZero(d1)) return d1;
RNScalar d2 = R2SignedDistance(line, box.Corner(quadrant));
if (RNIsNegative(d2)) return d2;
else return 0.0;
}
RNBoolean R3Contains(const R3Halfspace& halfspace, const R3Circle& circle)
{
// Return whether halfspace contains circle
RNScalar d = R3SignedDistance(halfspace.Plane(), circle.Center());
if (RNIsNegative(d)) return FALSE;
else if (RNIsGreater(d, circle.Radius())) return TRUE;
else {
RNScalar cos_theta = halfspace.Plane().Normal().Dot(circle.Normal());
if (cos_theta < 0.0) cos_theta = halfspace.Plane().Normal().Dot(-circle.Normal());
return (RNIsGreaterOrEqual(d, cos_theta * circle.Radius()));
}
}
RNLength R2SignedDistance(const R2Line& line, const R2Span& span)
{
// Return signed distance from line to span
RNLength d1 = R2SignedDistance(line, span.Start());
if (RNIsPositive(d1)) {
// Start point is above line
RNLength d2 = R2SignedDistance(line, span.End());
if (RNIsPositive(d2)) return ((d1 > d2) ? d2 : d1);
else return 0.0;
}
else if (RNIsNegative(d1)) {
// Start point is below line
RNLength d2 = R2SignedDistance(line, span.End());
if (RNIsNegative(d2)) return ((d1 > d2) ? d1 : d2);
else return 0.0;
}
else {
// Start point is on line
return 0.0;
}
}
RNBoolean R3Contains(const R3Cylinder& cylinder, const R3Point& point)
{
// Get cylinder axis
const R3Span& axis = cylinder.Axis();
// Check if outside top or bottom
RNScalar t = axis.T(point);
if (RNIsNegative(t) || RNIsGreater(t, axis.Length()))
return FALSE;
// Check if inside radius
RNLength d = R3Distance(point, axis.Point(t));
return (RNIsLessOrEqual(d, cylinder.Radius()));
}
RNBoolean R3Contains(const R3Cone& cone, const R3Point& point)
{
// Get cone axis
const R3Span& axis = cone.Axis();
// Check if outside top or bottom
RNScalar t = axis.T(point);
if (RNIsNegative(t) || RNIsGreater(t, axis.Length()))
return FALSE;
// Check if inside radius
RNLength r = (1.0 - t / axis.Length()) * cone.Radius();
RNLength d = R3Distance(axis.Point(t), point);
return RNIsGreaterOrEqual(r, d);
}
RNBoolean R3Contains(const R3Triangle& triangle, const R3Point& point)
{
// Check whether triangle bounding shape contains point
if (!R3Contains(triangle.Box(), point)) return FALSE;
// Check whether triangle plane contains point
if (!R3Contains(triangle.Plane(), point)) return FALSE;
// Compute whether point is on correct side of each edge
const R3Point& p0 = triangle.Vertex(0)->Position();
const R3Point& p1 = triangle.Vertex(1)->Position();
const R3Point& p2 = triangle.Vertex(2)->Position();
R3Plane h01(p1, triangle.Normal(), p1 - p0);
if (RNIsNegative(R3SignedDistance(h01, point))) return FALSE;
R3Plane plane01(p1, triangle.Normal(), p1 - p0);
if (RNIsNegative(R3SignedDistance(plane01, point))) return FALSE;
R3Plane plane12(p2, triangle.Normal(), p2 - p1);
if (RNIsNegative(R3SignedDistance(plane12, point))) return FALSE;
R3Plane plane20(p0, triangle.Normal(), p0 - p2);
if (RNIsNegative(R3SignedDistance(plane20, point))) return FALSE;
// Triangle contains point
return TRUE;
}
RNLength R2Distance(const R2Point& point, const R2Span& span)
{
// Check span
if (RNIsZero(span.Length())) return R2Distance(point, span.Start());
// Check if start point is closest
R2Vector v1 = point - span.Start();
RNScalar dir1 = v1.Dot(span.Vector());
if (RNIsNegative(dir1)) return v1.Length();
// Check if end point is closest
R2Vector v2 = point - span.End();
RNScalar dir2 = v2.Dot(span.Vector());
if (RNIsPositive(dir2)) return v2.Length();
// Return distance from point to span line
return R2Distance(point, span.Line());
}