static bool IsOutside(Vector3 v, Cylinder3 cylinder) { var centerProject = ProjectOnPlane(v, -cylinder.AxisDirection, cylinder.Origin); var pv = v - centerProject; if (pv.Length() >= cylinder.Radius) { return(true); } return(false); }
static Result LineIntersection(Vector3 lineOrigin, Vector3 line, Cylinder3 cylinder) { var result = new Result(); var direction = line.Normalized(); var length = line.Length(); RayIntersection(lineOrigin, direction, cylinder, result); for (int i = 0; i < result.numIntersections; ++i) { if (length >= result.parameter[i] && result.parameter[i] > 0) { result.point.Add(lineOrigin + result.parameter[i] * direction); } } return(result); }
static bool EndgeIntersec(Vector3 v, Vector3 edge, Cylinder3 c, ref List <Vector3> pp) { if (Math.Abs(Math.Abs(Vector3.Dot(edge.Normalized(), -c.AxisDirection)) - 1) < 0.001) { //edge is colinear to cylinder asis return(false); } var res = LineIntersection(v, edge, c); if (IsOutside(v, c)) { pp.Add(v); } if (res.point.Any()) { pp.Add(res.point[0]); return(true); } return(false); }
static void RayIntersection(Vector3 lineOrigin, Vector3 lineDirection, Cylinder3 cylinder, Result result) { // Initialize the result as if there is no intersection. If we discover // an intersection, these values will be modified accordingly. result.intersect = false; result.numIntersections = 0; // Create a coordinate system for the cylinder. In this system, the // cylinder segment center C is the origin and the cylinder axis direction // W is the z-axis. U and V are the other coordinate axis directions. // If P = x*U+y*V+z*W, the cylinder is x^2 + y^2 = r^2, where r is the // cylinder radius. The end caps are |z| = h/2, where h is the cylinder // height. Vector3[] basis = new Vector3[3]; // {W, U, V} basis[0] = cylinder.AxisDirection; ComputeOrthogonalComplement(1, basis, false); var halfHeight = 0.5f * cylinder.Height; var rSqr = cylinder.Radius * cylinder.Radius; // Convert incoming line origin to capsule coordinates. Vector3 diff = lineOrigin - cylinder.Origin; var P = new Vector3( Vector3.Dot(basis[1], diff), Vector3.Dot(basis[2], diff), Vector3.Dot(basis[0], diff)); // Get the z-value, in cylinder coordinates, of the incoming line's // unit-length direction. var dz = Vector3.Dot(basis[0], lineDirection); if (Math.Abs(dz) == 1f) { // The line is parallel to the cylinder axis. Determine whether the // line intersects the cylinder end disks. var radialSqrDist = rSqr - P[0] * P[0] - P[1] * P[1]; if (radialSqrDist >= 0f) { // The line intersects the cylinder end disks. result.intersect = true; result.numIntersections = 2; if (dz > 0f) { result.parameter[0] = -P[2] - halfHeight; result.parameter[1] = -P[2] + halfHeight; } else { result.parameter[0] = P[2] - halfHeight; result.parameter[1] = P[2] + halfHeight; } } // else: The line is outside the cylinder, no intersection. return; } // Convert the incoming line unit-length direction to cylinder // coordinates. var D = new Vector3(Vector3.Dot(basis[1], lineDirection), Vector3.Dot(basis[2], lineDirection), dz); float a0, a1, a2, discr, root, inv, tValue; if (D[2] == 0f) { // The line is perpendicular to the cylinder axis. if (Math.Abs(P[2]) <= halfHeight) { // Test intersection of line P+t*D with infinite cylinder // x^2+y^2 = r^2. This reduces to computing the roots of a // quadratic equation. If P = (px,py,pz) and D = (dx,dy,dz), // then the quadratic equation is // (dx^2+dy^2)*t^2 + 2*(px*dx+py*dy)*t + (px^2+py^2-r^2) = 0 a0 = P[0] * P[0] + P[1] * P[1] - rSqr; a1 = P[0] * D[0] + P[1] * D[1]; a2 = D[0] * D[0] + D[1] * D[1]; discr = a1 * a1 - a0 * a2; if (discr > 0) { // The line intersects the cylinder in two places. result.intersect = true; result.numIntersections = 2; root = (float)Math.Sqrt(discr); inv = 1f / a2; result.parameter[0] = (-a1 - root) * inv; result.parameter[1] = (-a1 + root) * inv; } else if (discr == 0) { // The line is tangent to the cylinder. result.intersect = true; result.numIntersections = 1; result.parameter[0] = -a1 / a2; // Used by derived classes. result.parameter[1] = result.parameter[0]; } // else: The line does not intersect the cylinder. } // else: The line is outside the planes of the cylinder end disks. return; } // Test for intersections with the planes of the end disks. inv = 1f / D[2]; var t0 = (-halfHeight - P[2]) * inv; var xTmp = P[0] + t0 * D[0]; var yTmp = P[1] + t0 * D[1]; if (xTmp * xTmp + yTmp * yTmp <= rSqr) { // Plane intersection inside the top cylinder end disk. result.parameter[result.numIntersections++] = t0; } var t1 = (+halfHeight - P[2]) * inv; xTmp = P[0] + t1 * D[0]; yTmp = P[1] + t1 * D[1]; if (xTmp * xTmp + yTmp * yTmp <= rSqr) { // Plane intersection inside the bottom cylinder end disk. result.parameter[result.numIntersections++] = t1; } if (result.numIntersections < 2) { // Test for intersection with the cylinder wall. a0 = P[0] * P[0] + P[1] * P[1] - rSqr; a1 = P[0] * D[0] + P[1] * D[1]; a2 = D[0] * D[0] + D[1] * D[1]; discr = a1 * a1 - a0 * a2; if (discr > 0) { root = (float)Math.Sqrt(discr); inv = 1f / a2; tValue = (-a1 - root) * inv; if (t0 <= t1) { if (t0 <= tValue && tValue <= t1) { result.parameter[result.numIntersections++] = tValue; } } else { if (t1 <= tValue && tValue <= t0) { result.parameter[result.numIntersections++] = tValue; } } if (result.numIntersections < 2) { tValue = (-a1 + root) * inv; if (t0 <= t1) { if (t0 <= tValue && tValue <= t1) { result.parameter[result.numIntersections++] = tValue; } } else { if (t1 <= tValue && tValue <= t0) { result.parameter[result.numIntersections++] = tValue; } } } // else: Line intersects end disk and cylinder wall. } else if (discr == 0) { tValue = -a1 / a2; if (t0 <= t1) { if (t0 <= tValue && tValue <= t1) { result.parameter[result.numIntersections++] = tValue; } } else { if (t1 <= tValue && tValue <= t0) { result.parameter[result.numIntersections++] = tValue; } } } // else: Line does not intersect cylinder wall. } // else: Line intersects both top and bottom cylinder end disks. if (result.numIntersections == 2) { result.intersect = true; if (result.parameter[0] > result.parameter[1]) { //std::swap(result.parameter[0], result.parameter[1]); var p0 = result.parameter[0]; result.parameter[0] = result.parameter[1]; result.parameter[1] = p0; } } else if (result.numIntersections == 1) { result.intersect = true; // Used by derived classes. result.parameter[1] = result.parameter[0]; } }