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