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diff --git a/thirdparty/thekla_atlas/nvmath/Sphere.cpp b/thirdparty/thekla_atlas/nvmath/Sphere.cpp
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+++ b/thirdparty/thekla_atlas/nvmath/Sphere.cpp
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+// 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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