// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2020
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt
// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// Version: 4.0.2019.08.13
#pragma once
#include <Mathematics/FIQuery.h>
#include <Mathematics/Cylinder3.h>
#include <Mathematics/Vector3.h>
// The queries consider the cylinder to be a solid.
namespace WwiseGTE
{
template <typename Real>
class FIQuery<Real, Line3<Real>, Cylinder3<Real>>
{
public:
struct Result
{
bool intersect;
int numIntersections;
std::array<Real, 2> parameter;
std::array<Vector3<Real>, 2> point;
};
Result operator()(Line3<Real> const& line, Cylinder3<Real> const& cylinder)
{
Result result;
DoQuery(line.origin, line.direction, cylinder, result);
for (int i = 0; i < result.numIntersections; ++i)
{
result.point[i] = line.origin + result.parameter[i] * line.direction;
}
return result;
}
protected:
void DoQuery(Vector3<Real> const& lineOrigin,
Vector3<Real> const& lineDirection, Cylinder3<Real> const& 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<Real> basis[3]; // {W, U, V}
basis[0] = cylinder.axis.direction;
ComputeOrthogonalComplement(1, basis);
Real halfHeight = (Real)0.5 * cylinder.height;
Real rSqr = cylinder.radius * cylinder.radius;
// Convert incoming line origin to capsule coordinates.
Vector3<Real> diff = lineOrigin - cylinder.axis.origin;
Vector3<Real> P{ Dot(basis[1], diff), Dot(basis[2], diff), Dot(basis[0], diff) };
// Get the z-value, in cylinder coordinates, of the incoming
// line's unit-length direction.
Real dz = Dot(basis[0], lineDirection);
if (std::fabs(dz) == (Real)1)
{
// The line is parallel to the cylinder axis. Determine
// whether the line intersects the cylinder end disks.
Real radialSqrDist = rSqr - P[0] * P[0] - P[1] * P[1];
if (radialSqrDist >= (Real)0)
{
// The line intersects the cylinder end disks.
result.intersect = true;
result.numIntersections = 2;
if (dz > (Real)0)
{
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.
Vector3<Real> D{ Dot(basis[1], lineDirection), Dot(basis[2], lineDirection), dz };
Real a0, a1, a2, discr, root, inv, tValue;
if (D[2] == (Real)0)
{
// The line is perpendicular to the cylinder axis.
if (std::fabs(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 > (Real)0)
{
// The line intersects the cylinder in two places.
result.intersect = true;
result.numIntersections = 2;
root = std::sqrt(discr);
inv = ((Real)1) / a2;
result.parameter[0] = (-a1 - root) * inv;
result.parameter[1] = (-a1 + root) * inv;
}
else if (discr == (Real)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 = (Real)1 / D[2];
Real t0 = (-halfHeight - P[2]) * inv;
Real xTmp = P[0] + t0 * D[0];
Real 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;
}
Real 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 > (Real)0)
{
root = std::sqrt(discr);
inv = (Real)1 / 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 == (Real)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]);
}
}
else if (result.numIntersections == 1)
{
result.intersect = true;
// Used by derived classes.
result.parameter[1] = result.parameter[0];
}
}
};
}