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249 lines
9.7 KiB
249 lines
9.7 KiB
// David Eberly, Geometric Tools, Redmond WA 98052
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// Copyright (c) 1998-2021
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// Distributed under the Boost Software License, Version 1.0.
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// https://www.boost.org/LICENSE_1_0.txt
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// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
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// Version: 4.0.2019.08.13
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#pragma once
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#include <Mathematics/FIQuery.h>
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#include <Mathematics/Cylinder3.h>
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#include <Mathematics/Vector3.h>
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// The queries consider the cylinder to be a solid.
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namespace gte
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{
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template <typename Real>
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class FIQuery<Real, Line3<Real>, Cylinder3<Real>>
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{
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public:
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struct Result
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{
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bool intersect;
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int numIntersections;
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std::array<Real, 2> parameter;
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std::array<Vector3<Real>, 2> point;
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};
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Result operator()(Line3<Real> const& line, Cylinder3<Real> const& cylinder)
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{
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Result result;
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DoQuery(line.origin, line.direction, cylinder, result);
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for (int i = 0; i < result.numIntersections; ++i)
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{
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result.point[i] = line.origin + result.parameter[i] * line.direction;
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}
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return result;
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}
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protected:
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void DoQuery(Vector3<Real> const& lineOrigin,
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Vector3<Real> const& lineDirection, Cylinder3<Real> const& cylinder,
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Result& result)
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{
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// Initialize the result as if there is no intersection. If we
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// discover an intersection, these values will be modified
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// accordingly.
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result.intersect = false;
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result.numIntersections = 0;
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// Create a coordinate system for the cylinder. In this system,
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// the cylinder segment center C is the origin and the cylinder
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// axis direction W is the z-axis. U and V are the other
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// coordinate axis directions. If P = x*U+y*V+z*W, the cylinder
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// is x^2 + y^2 = r^2, where r is the cylinder radius. The end
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// caps are |z| = h/2, where h is the cylinder height.
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Vector3<Real> basis[3]; // {W, U, V}
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basis[0] = cylinder.axis.direction;
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ComputeOrthogonalComplement(1, basis);
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Real halfHeight = (Real)0.5 * cylinder.height;
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Real rSqr = cylinder.radius * cylinder.radius;
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// Convert incoming line origin to capsule coordinates.
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Vector3<Real> diff = lineOrigin - cylinder.axis.origin;
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Vector3<Real> P{ Dot(basis[1], diff), Dot(basis[2], diff), Dot(basis[0], diff) };
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// Get the z-value, in cylinder coordinates, of the incoming
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// line's unit-length direction.
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Real dz = Dot(basis[0], lineDirection);
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if (std::fabs(dz) == (Real)1)
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{
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// The line is parallel to the cylinder axis. Determine
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// whether the line intersects the cylinder end disks.
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Real radialSqrDist = rSqr - P[0] * P[0] - P[1] * P[1];
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if (radialSqrDist >= (Real)0)
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{
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// The line intersects the cylinder end disks.
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result.intersect = true;
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result.numIntersections = 2;
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if (dz > (Real)0)
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{
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result.parameter[0] = -P[2] - halfHeight;
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result.parameter[1] = -P[2] + halfHeight;
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}
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else
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{
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result.parameter[0] = P[2] - halfHeight;
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result.parameter[1] = P[2] + halfHeight;
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}
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}
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// else: The line is outside the cylinder, no intersection.
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return;
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}
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// Convert the incoming line unit-length direction to cylinder
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// coordinates.
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Vector3<Real> D{ Dot(basis[1], lineDirection), Dot(basis[2], lineDirection), dz };
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Real a0, a1, a2, discr, root, inv, tValue;
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if (D[2] == (Real)0)
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{
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// The line is perpendicular to the cylinder axis.
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if (std::fabs(P[2]) <= halfHeight)
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{
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// Test intersection of line P+t*D with infinite cylinder
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// x^2+y^2 = r^2. This reduces to computing the roots of
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// a quadratic equation. If P = (px,py,pz) and
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// D = (dx,dy,dz), then the quadratic equation is
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// (dx^2+dy^2)*t^2 + 2*(px*dx+py*dy)*t
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// + (px^2+py^2-r^2) = 0
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a0 = P[0] * P[0] + P[1] * P[1] - rSqr;
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a1 = P[0] * D[0] + P[1] * D[1];
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a2 = D[0] * D[0] + D[1] * D[1];
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discr = a1 * a1 - a0 * a2;
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if (discr > (Real)0)
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{
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// The line intersects the cylinder in two places.
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result.intersect = true;
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result.numIntersections = 2;
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root = std::sqrt(discr);
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inv = ((Real)1) / a2;
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result.parameter[0] = (-a1 - root) * inv;
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result.parameter[1] = (-a1 + root) * inv;
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}
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else if (discr == (Real)0)
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{
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// The line is tangent to the cylinder.
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result.intersect = true;
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result.numIntersections = 1;
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result.parameter[0] = -a1 / a2;
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// Used by derived classes.
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result.parameter[1] = result.parameter[0];
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}
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// else: The line does not intersect the cylinder.
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}
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// else: The line is outside the planes of the cylinder end
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// disks.
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return;
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}
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// Test for intersections with the planes of the end disks.
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inv = (Real)1 / D[2];
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Real t0 = (-halfHeight - P[2]) * inv;
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Real xTmp = P[0] + t0 * D[0];
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Real yTmp = P[1] + t0 * D[1];
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if (xTmp * xTmp + yTmp * yTmp <= rSqr)
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{
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// Plane intersection inside the top cylinder end disk.
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result.parameter[result.numIntersections++] = t0;
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}
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Real t1 = (+halfHeight - P[2]) * inv;
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xTmp = P[0] + t1 * D[0];
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yTmp = P[1] + t1 * D[1];
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if (xTmp * xTmp + yTmp * yTmp <= rSqr)
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{
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// Plane intersection inside the bottom cylinder end disk.
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result.parameter[result.numIntersections++] = t1;
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}
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if (result.numIntersections < 2)
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{
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// Test for intersection with the cylinder wall.
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a0 = P[0] * P[0] + P[1] * P[1] - rSqr;
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a1 = P[0] * D[0] + P[1] * D[1];
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a2 = D[0] * D[0] + D[1] * D[1];
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discr = a1 * a1 - a0 * a2;
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if (discr > (Real)0)
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{
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root = std::sqrt(discr);
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inv = (Real)1 / a2;
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tValue = (-a1 - root) * inv;
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if (t0 <= t1)
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{
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if (t0 <= tValue && tValue <= t1)
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{
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result.parameter[result.numIntersections++] = tValue;
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}
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}
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else
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{
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if (t1 <= tValue && tValue <= t0)
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{
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result.parameter[result.numIntersections++] = tValue;
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}
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}
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if (result.numIntersections < 2)
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{
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tValue = (-a1 + root) * inv;
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if (t0 <= t1)
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{
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if (t0 <= tValue && tValue <= t1)
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{
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result.parameter[result.numIntersections++] = tValue;
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}
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}
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else
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{
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if (t1 <= tValue && tValue <= t0)
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{
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result.parameter[result.numIntersections++] = tValue;
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}
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}
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}
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// else: Line intersects end disk and cylinder wall.
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}
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else if (discr == (Real)0)
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{
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tValue = -a1 / a2;
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if (t0 <= t1)
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{
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if (t0 <= tValue && tValue <= t1)
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{
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result.parameter[result.numIntersections++] = tValue;
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}
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}
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else
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{
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if (t1 <= tValue && tValue <= t0)
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{
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result.parameter[result.numIntersections++] = tValue;
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}
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}
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}
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// else: Line does not intersect cylinder wall.
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}
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// else: Line intersects both top and bottom cylinder end disks.
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if (result.numIntersections == 2)
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{
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result.intersect = true;
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if (result.parameter[0] > result.parameter[1])
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{
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std::swap(result.parameter[0], result.parameter[1]);
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}
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}
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else if (result.numIntersections == 1)
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{
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result.intersect = true;
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// Used by derived classes.
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result.parameter[1] = result.parameter[0];
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}
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}
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};
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}
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