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-rw-r--r--thirdparty/thekla_atlas/nvmath/Sphere.cpp431
1 files changed, 0 insertions, 431 deletions
diff --git a/thirdparty/thekla_atlas/nvmath/Sphere.cpp b/thirdparty/thekla_atlas/nvmath/Sphere.cpp
deleted file mode 100644
index e0c1ad652c..0000000000
--- a/thirdparty/thekla_atlas/nvmath/Sphere.cpp
+++ /dev/null
@@ -1,431 +0,0 @@
-// This code is in the public domain -- Ignacio Castaņo <castano@gmail.com>
-
-#include "Sphere.h"
-#include "Vector.inl"
-#include "Box.inl"
-
-#include <float.h> // FLT_MAX
-
-using namespace nv;
-
-const float radiusEpsilon = 1e-4f;
-
-Sphere::Sphere(Vector3::Arg p0, Vector3::Arg p1)
-{
- if (p0 == p1) *this = Sphere(p0);
- else {
- center = (p0 + p1) * 0.5f;
- radius = length(p0 - center) + radiusEpsilon;
-
- float d0 = length(p0 - center);
- float d1 = length(p1 - center);
- nvDebugCheck(equal(d0, radius - radiusEpsilon));
- nvDebugCheck(equal(d1, radius - radiusEpsilon));
- }
-}
-
-Sphere::Sphere(Vector3::Arg p0, Vector3::Arg p1, Vector3::Arg p2)
-{
- if (p0 == p1 || p0 == p2) *this = Sphere(p1, p2);
- else if (p1 == p2) *this = Sphere(p0, p2);
- else {
- Vector3 a = p1 - p0;
- Vector3 b = p2 - p0;
- Vector3 c = cross(a, b);
-
- float denominator = 2.0f * lengthSquared(c);
-
- if (!isZero(denominator)) {
- Vector3 d = (lengthSquared(b) * cross(c, a) + lengthSquared(a) * cross(b, c)) / denominator;
-
- center = p0 + d;
- radius = length(d) + radiusEpsilon;
-
- float d0 = length(p0 - center);
- float d1 = length(p1 - center);
- float d2 = length(p2 - center);
- nvDebugCheck(equal(d0, radius - radiusEpsilon));
- nvDebugCheck(equal(d1, radius - radiusEpsilon));
- nvDebugCheck(equal(d2, radius - radiusEpsilon));
- }
- else {
- // @@ This is a specialization of the code below, but really, the only thing we need to do here is to find the two most distant points.
- // Compute all possible spheres, invalidate those that do not contain the four points, keep the smallest.
- Sphere s0(p1, p2);
- float d0 = distanceSquared(s0, p0);
- if (d0 > 0) s0.radius = NV_FLOAT_MAX;
-
- Sphere s1(p0, p2);
- float d1 = distanceSquared(s1, p1);
- if (d1 > 0) s1.radius = NV_FLOAT_MAX;
-
- Sphere s2(p0, p1);
- float d2 = distanceSquared(s2, p2);
- if (d2 > 0) s1.radius = NV_FLOAT_MAX;
-
- if (s0.radius < s1.radius && s0.radius < s2.radius) {
- center = s0.center;
- radius = s0.radius;
- }
- else if (s1.radius < s2.radius) {
- center = s1.center;
- radius = s1.radius;
- }
- else {
- center = s2.center;
- radius = s2.radius;
- }
- }
- }
-}
-
-Sphere::Sphere(Vector3::Arg p0, Vector3::Arg p1, Vector3::Arg p2, Vector3::Arg p3)
-{
- if (p0 == p1 || p0 == p2 || p0 == p3) *this = Sphere(p1, p2, p3);
- else if (p1 == p2 || p1 == p3) *this = Sphere(p0, p2, p3);
- else if (p2 == p3) *this = Sphere(p0, p1, p2);
- else {
- // @@ This only works if the points are not coplanar!
- Vector3 a = p1 - p0;
- Vector3 b = p2 - p0;
- Vector3 c = p3 - p0;
-
- float denominator = 2.0f * dot(c, cross(a, b)); // triple product.
-
- if (!isZero(denominator)) {
- Vector3 d = (lengthSquared(c) * cross(a, b) + lengthSquared(b) * cross(c, a) + lengthSquared(a) * cross(b, c)) / denominator;
-
- center = p0 + d;
- radius = length(d) + radiusEpsilon;
-
- float d0 = length(p0 - center);
- float d1 = length(p1 - center);
- float d2 = length(p2 - center);
- float d3 = length(p3 - center);
- nvDebugCheck(equal(d0, radius - radiusEpsilon));
- nvDebugCheck(equal(d1, radius - radiusEpsilon));
- nvDebugCheck(equal(d2, radius - radiusEpsilon));
- nvDebugCheck(equal(d3, radius - radiusEpsilon));
- }
- else {
- // Compute all possible spheres, invalidate those that do not contain the four points, keep the smallest.
- Sphere s0(p1, p2, p3);
- float d0 = distanceSquared(s0, p0);
- if (d0 > 0) s0.radius = NV_FLOAT_MAX;
-
- Sphere s1(p0, p2, p3);
- float d1 = distanceSquared(s1, p1);
- if (d1 > 0) s1.radius = NV_FLOAT_MAX;
-
- Sphere s2(p0, p1, p3);
- float d2 = distanceSquared(s2, p2);
- if (d2 > 0) s2.radius = NV_FLOAT_MAX;
-
- Sphere s3(p0, p1, p2);
- float d3 = distanceSquared(s3, p3);
- if (d3 > 0) s2.radius = NV_FLOAT_MAX;
-
- if (s0.radius < s1.radius && s0.radius < s2.radius && s0.radius < s3.radius) {
- center = s0.center;
- radius = s0.radius;
- }
- else if (s1.radius < s2.radius && s1.radius < s3.radius) {
- center = s1.center;
- radius = s1.radius;
- }
- else if (s1.radius < s3.radius) {
- center = s2.center;
- radius = s2.radius;
- }
- else {
- center = s3.center;
- radius = s3.radius;
- }
- }
- }
-}
-
-
-float nv::distanceSquared(const Sphere & sphere, const Vector3 & point)
-{
- return lengthSquared(sphere.center - point) - square(sphere.radius);
-}
-
-
-
-// Implementation of "MiniBall" based on:
-// http://www.flipcode.com/archives/Smallest_Enclosing_Spheres.shtml
-
-static Sphere recurseMini(const Vector3 *P[], uint p, uint b = 0)
-{
- Sphere MB;
-
- switch(b)
- {
- case 0:
- MB = Sphere(*P[0]);
- break;
- case 1:
- MB = Sphere(*P[-1]);
- break;
- case 2:
- MB = Sphere(*P[-1], *P[-2]);
- break;
- case 3:
- MB = Sphere(*P[-1], *P[-2], *P[-3]);
- break;
- case 4:
- MB = Sphere(*P[-1], *P[-2], *P[-3], *P[-4]);
- return MB;
- }
-
- for (uint i = 0; i < p; i++)
- {
- if (distanceSquared(MB, *P[i]) > 0) // Signed square distance to sphere
- {
- for (uint j = i; j > 0; j--)
- {
- swap(P[j], P[j-1]);
- }
-
- MB = recurseMini(P + 1, i, b + 1);
- }
- }
-
- return MB;
-}
-
-static bool allInside(const Sphere & sphere, const Vector3 * pointArray, const uint pointCount) {
- for (uint i = 0; i < pointCount; i++) {
- if (distanceSquared(sphere, pointArray[i]) >= NV_EPSILON) {
- return false;
- }
- }
- return true;
-}
-
-
-Sphere nv::miniBall(const Vector3 * pointArray, const uint pointCount)
-{
- nvDebugCheck(pointArray != NULL);
- nvDebugCheck(pointCount > 0);
-
- const Vector3 **L = new const Vector3*[pointCount];
-
- for (uint i = 0; i < pointCount; i++) {
- L[i] = &pointArray[i];
- }
-
- Sphere sphere = recurseMini(L, pointCount);
-
- delete [] L;
-
- nvDebugCheck(allInside(sphere, pointArray, pointCount));
-
- return sphere;
-}
-
-
-// Approximate bounding sphere, based on "An Efficient Bounding Sphere" by Jack Ritter, from "Graphics Gems"
-Sphere nv::approximateSphere_Ritter(const Vector3 * pointArray, const uint pointCount)
-{
- nvDebugCheck(pointArray != NULL);
- nvDebugCheck(pointCount > 0);
-
- Vector3 xmin, xmax, ymin, ymax, zmin, zmax;
-
- xmin = xmax = ymin = ymax = zmin = zmax = pointArray[0];
-
- // FIRST PASS: find 6 minima/maxima points
- xmin.x = ymin.y = zmin.z = FLT_MAX;
- xmax.x = ymax.y = zmax.z = -FLT_MAX;
-
- for (uint i = 0; i < pointCount; i++)
- {
- const Vector3 & p = pointArray[i];
- if (p.x < xmin.x) xmin = p;
- if (p.x > xmax.x) xmax = p;
- if (p.y < ymin.y) ymin = p;
- if (p.y > ymax.y) ymax = p;
- if (p.z < zmin.z) zmin = p;
- if (p.z > zmax.z) zmax = p;
- }
-
- float xspan = lengthSquared(xmax - xmin);
- float yspan = lengthSquared(ymax - ymin);
- float zspan = lengthSquared(zmax - zmin);
-
- // Set points dia1 & dia2 to the maximally separated pair.
- Vector3 dia1 = xmin;
- Vector3 dia2 = xmax;
- float maxspan = xspan;
- if (yspan > maxspan) {
- maxspan = yspan;
- dia1 = ymin;
- dia2 = ymax;
- }
- if (zspan > maxspan) {
- dia1 = zmin;
- dia2 = zmax;
- }
-
- // |dia1-dia2| is a diameter of initial sphere
-
- // calc initial center
- Sphere sphere;
- sphere.center = (dia1 + dia2) / 2.0f;
-
- // calculate initial radius**2 and radius
- float rad_sq = lengthSquared(dia2 - sphere.center);
- sphere.radius = sqrtf(rad_sq);
-
-
- // SECOND PASS: increment current sphere
- for (uint i = 0; i < pointCount; i++)
- {
- const Vector3 & p = pointArray[i];
-
- float old_to_p_sq = lengthSquared(p - sphere.center);
-
- if (old_to_p_sq > rad_sq) // do r**2 test first
- {
- // this point is outside of current sphere
- float old_to_p = sqrtf(old_to_p_sq);
-
- // calc radius of new sphere
- sphere.radius = (sphere.radius + old_to_p) / 2.0f;
- rad_sq = sphere.radius * sphere.radius; // for next r**2 compare
-
- float old_to_new = old_to_p - sphere.radius;
-
- // calc center of new sphere
- sphere.center = (sphere.radius * sphere.center + old_to_new * p) / old_to_p;
- }
- }
-
- nvDebugCheck(allInside(sphere, pointArray, pointCount));
-
- return sphere;
-}
-
-
-static float computeSphereRadius(const Vector3 & center, const Vector3 * pointArray, const uint pointCount) {
-
- float maxRadius2 = 0;
-
- for (uint i = 0; i < pointCount; i++)
- {
- const Vector3 & p = pointArray[i];
-
- float r2 = lengthSquared(center - p);
-
- if (r2 > maxRadius2) {
- maxRadius2 = r2;
- }
- }
-
- return sqrtf(maxRadius2) + radiusEpsilon;
-}
-
-
-Sphere nv::approximateSphere_AABB(const Vector3 * pointArray, const uint pointCount)
-{
- nvDebugCheck(pointArray != NULL);
- nvDebugCheck(pointCount > 0);
-
- Box box;
- box.clearBounds();
-
- for (uint i = 0; i < pointCount; i++) {
- box.addPointToBounds(pointArray[i]);
- }
-
- Sphere sphere;
- sphere.center = box.center();
- sphere.radius = computeSphereRadius(sphere.center, pointArray, pointCount);
-
- nvDebugCheck(allInside(sphere, pointArray, pointCount));
-
- return sphere;
-}
-
-
-static void computeExtremalPoints(const Vector3 & dir, const Vector3 * pointArray, uint pointCount, Vector3 * minPoint, Vector3 * maxPoint) {
- nvDebugCheck(pointCount > 0);
-
- uint mini = 0;
- uint maxi = 0;
- float minDist = FLT_MAX;
- float maxDist = -FLT_MAX;
-
- for (uint i = 0; i < pointCount; i++) {
- float d = dot(dir, pointArray[i]);
-
- if (d < minDist) {
- minDist = d;
- mini = i;
- }
- if (d > maxDist) {
- maxDist = d;
- maxi = i;
- }
- }
- nvDebugCheck(minDist != FLT_MAX);
- nvDebugCheck(maxDist != -FLT_MAX);
-
- *minPoint = pointArray[mini];
- *maxPoint = pointArray[maxi];
-}
-
-// EPOS algorithm based on:
-// http://www.ep.liu.se/ecp/034/009/ecp083409.pdf
-Sphere nv::approximateSphere_EPOS6(const Vector3 * pointArray, uint pointCount)
-{
- nvDebugCheck(pointArray != NULL);
- nvDebugCheck(pointCount > 0);
-
- Vector3 extremalPoints[6];
-
- // Compute 6 extremal points.
- computeExtremalPoints(Vector3(1, 0, 0), pointArray, pointCount, extremalPoints+0, extremalPoints+1);
- computeExtremalPoints(Vector3(0, 1, 0), pointArray, pointCount, extremalPoints+2, extremalPoints+3);
- computeExtremalPoints(Vector3(0, 0, 1), pointArray, pointCount, extremalPoints+4, extremalPoints+5);
-
- Sphere sphere = miniBall(extremalPoints, 6);
- sphere.radius = computeSphereRadius(sphere.center, pointArray, pointCount);
-
- nvDebugCheck(allInside(sphere, pointArray, pointCount));
-
- return sphere;
-}
-
-Sphere nv::approximateSphere_EPOS14(const Vector3 * pointArray, uint pointCount)
-{
- nvDebugCheck(pointArray != NULL);
- nvDebugCheck(pointCount > 0);
-
- Vector3 extremalPoints[14];
-
- // Compute 14 extremal points.
- computeExtremalPoints(Vector3(1, 0, 0), pointArray, pointCount, extremalPoints+0, extremalPoints+1);
- computeExtremalPoints(Vector3(0, 1, 0), pointArray, pointCount, extremalPoints+2, extremalPoints+3);
- computeExtremalPoints(Vector3(0, 0, 1), pointArray, pointCount, extremalPoints+4, extremalPoints+5);
-
- float d = sqrtf(1.0f/3.0f);
-
- computeExtremalPoints(Vector3(d, d, d), pointArray, pointCount, extremalPoints+6, extremalPoints+7);
- computeExtremalPoints(Vector3(-d, d, d), pointArray, pointCount, extremalPoints+8, extremalPoints+9);
- computeExtremalPoints(Vector3(-d, -d, d), pointArray, pointCount, extremalPoints+10, extremalPoints+11);
- computeExtremalPoints(Vector3(d, -d, d), pointArray, pointCount, extremalPoints+12, extremalPoints+13);
-
-
- Sphere sphere = miniBall(extremalPoints, 14);
- sphere.radius = computeSphereRadius(sphere.center, pointArray, pointCount);
-
- nvDebugCheck(allInside(sphere, pointArray, pointCount));
-
- return sphere;
-}
-
-
-
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