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// // SPDX-License-Identifier: BSD-3-Clause // Copyright Contributors to the OpenEXR Project. // // // Algorithms applied to or in conjunction with Imath::Line class // #ifndef INCLUDED_IMATHLINEALGO_H #define INCLUDED_IMATHLINEALGO_H #include "ImathFun.h" #include "ImathLine.h" #include "ImathNamespace.h" #include "ImathVecAlgo.h" IMATH_INTERNAL_NAMESPACE_HEADER_ENTER /// /// Compute point1 and point2 such that point1 is on line1, point2 /// is on line2 and the distance between point1 and point2 is minimal. /// /// This function returns true if point1 and point2 can be computed, /// or false if line1 and line2 are parallel or nearly parallel. /// This function assumes that line1.dir and line2.dir are normalized. /// template IMATH_CONSTEXPR14 bool closestPoints ( const Line3& line1, const Line3& line2, Vec3& point1, Vec3& point2) IMATH_NOEXCEPT { Vec3 w = line1.pos - line2.pos; T d1w = line1.dir ^ w; T d2w = line2.dir ^ w; T d1d2 = line1.dir ^ line2.dir; T n1 = d1d2 * d2w - d1w; T n2 = d2w - d1d2 * d1w; T d = 1 - d1d2 * d1d2; T absD = abs (d); if ((absD > 1) || (abs (n1) < std::numeric_limits::max () * absD && abs (n2) < std::numeric_limits::max () * absD)) { point1 = line1 (n1 / d); point2 = line2 (n2 / d); return true; } else { return false; } } /// /// Given a line and a triangle (v0, v1, v2), the intersect() function /// finds the intersection of the line and the plane that contains the /// triangle. /// /// If the intersection point cannot be computed, either because the /// line and the triangle's plane are nearly parallel or because the /// triangle's area is very small, intersect() returns false. /// /// If the intersection point is outside the triangle, intersect /// returns false. /// /// If the intersection point, pt, is inside the triangle, intersect() /// computes a front-facing flag and the barycentric coordinates of /// the intersection point, and returns true. /// /// The front-facing flag is true if the dot product of the triangle's /// normal, (v2-v1)%(v1-v0), and the line's direction is negative. /// /// The barycentric coordinates have the following property: /// /// pt = v0 * barycentric.x + v1 * barycentric.y + v2 * barycentric.z /// template IMATH_CONSTEXPR14 bool intersect ( const Line3& line, const Vec3& v0, const Vec3& v1, const Vec3& v2, Vec3& pt, Vec3& barycentric, bool& front) IMATH_NOEXCEPT { Vec3 edge0 = v1 - v0; Vec3 edge1 = v2 - v1; Vec3 normal = edge1 % edge0; T l = normal.length (); if (l != 0) normal /= l; else return false; // zero-area triangle // // d is the distance of line.pos from the plane that contains the triangle. // The intersection point is at line.pos + (d/nd) * line.dir. // T d = normal ^ (v0 - line.pos); T nd = normal ^ line.dir; if (abs (nd) > 1 || abs (d) < std::numeric_limits::max () * abs (nd)) pt = line (d / nd); else return false; // line and plane are nearly parallel // // Compute the barycentric coordinates of the intersection point. // The intersection is inside the triangle if all three barycentric // coordinates are between zero and one. // { Vec3 en = edge0.normalized (); Vec3 a = pt - v0; Vec3 b = v2 - v0; Vec3 c = (a - en * (en ^ a)); Vec3 d = (b - en * (en ^ b)); T e = c ^ d; T f = d ^ d; if (e >= 0 && e <= f) barycentric.z = e / f; else return false; // outside } { Vec3 en = edge1.normalized (); Vec3 a = pt - v1; Vec3 b = v0 - v1; Vec3 c = (a - en * (en ^ a)); Vec3 d = (b - en * (en ^ b)); T e = c ^ d; T f = d ^ d; if (e >= 0 && e <= f) barycentric.x = e / f; else return false; // outside } barycentric.y = 1 - barycentric.x - barycentric.z; if (barycentric.y < 0) return false; // outside front = ((line.dir ^ normal) < 0); return true; } /// /// Return the vertex that is closest to the given line. The returned /// point is either v0, v1, or v2. /// template IMATH_CONSTEXPR14 Vec3 closestVertex ( const Vec3& v0, const Vec3& v1, const Vec3& v2, const Line3& l) IMATH_NOEXCEPT { Vec3 nearest = v0; T neardot = (v0 - l.closestPointTo (v0)).length2 (); T tmp = (v1 - l.closestPointTo (v1)).length2 (); if (tmp < neardot) { neardot = tmp; nearest = v1; } tmp = (v2 - l.closestPointTo (v2)).length2 (); if (tmp < neardot) { neardot = tmp; nearest = v2; } return nearest; } /// /// Rotate the point p around the line l by the given angle. /// template IMATH_CONSTEXPR14 Vec3 rotatePoint (const Vec3 p, Line3 l, T angle) IMATH_NOEXCEPT { // // Form a coordinate frame with . The rotation is the in xy // plane. // Vec3 q = l.closestPointTo (p); Vec3 x = p - q; T radius = x.length (); x.normalize (); Vec3 y = (x % l.dir).normalize (); T cosangle = std::cos (angle); T sinangle = std::sin (angle); Vec3 r = q + x * radius * cosangle + y * radius * sinangle; return r; } IMATH_INTERNAL_NAMESPACE_HEADER_EXIT #endif // INCLUDED_IMATHLINEALGO_H