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-rw-r--r--thirdparty/thekla_atlas/nvmath/Basis.cpp270
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diff --git a/thirdparty/thekla_atlas/nvmath/Basis.cpp b/thirdparty/thekla_atlas/nvmath/Basis.cpp
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+// This code is in the public domain -- Ignacio Castaņo <castano@gmail.com>
+
+#include "Basis.h"
+
+using namespace nv;
+
+
+/// Normalize basis vectors.
+void Basis::normalize(float epsilon /*= NV_EPSILON*/)
+{
+ normal = ::normalizeSafe(normal, Vector3(0.0f), epsilon);
+ tangent = ::normalizeSafe(tangent, Vector3(0.0f), epsilon);
+ bitangent = ::normalizeSafe(bitangent, Vector3(0.0f), epsilon);
+}
+
+
+/// Gram-Schmidt orthogonalization.
+/// @note Works only if the vectors are close to orthogonal.
+void Basis::orthonormalize(float epsilon /*= NV_EPSILON*/)
+{
+ // N' = |N|
+ // T' = |T - (N' dot T) N'|
+ // B' = |B - (N' dot B) N' - (T' dot B) T'|
+
+ normal = ::normalize(normal, epsilon);
+
+ tangent -= normal * dot(normal, tangent);
+ tangent = ::normalize(tangent, epsilon);
+
+ bitangent -= normal * dot(normal, bitangent);
+ bitangent -= tangent * dot(tangent, bitangent);
+ bitangent = ::normalize(bitangent, epsilon);
+}
+
+
+
+
+/// Robust orthonormalization.
+/// Returns an orthonormal basis even when the original is degenerate.
+void Basis::robustOrthonormalize(float epsilon /*= NV_EPSILON*/)
+{
+ // Normalize all vectors.
+ normalize(epsilon);
+
+ if (lengthSquared(normal) < epsilon*epsilon)
+ {
+ // Build normal from tangent and bitangent.
+ normal = cross(tangent, bitangent);
+
+ if (lengthSquared(normal) < epsilon*epsilon)
+ {
+ // Arbitrary basis.
+ tangent = Vector3(1, 0, 0);
+ bitangent = Vector3(0, 1, 0);
+ normal = Vector3(0, 0, 1);
+ return;
+ }
+
+ normal = nv::normalize(normal, epsilon);
+ }
+
+ // Project tangents to normal plane.
+ tangent -= normal * dot(normal, tangent);
+ bitangent -= normal * dot(normal, bitangent);
+
+ if (lengthSquared(tangent) < epsilon*epsilon)
+ {
+ if (lengthSquared(bitangent) < epsilon*epsilon)
+ {
+ // Arbitrary basis.
+ buildFrameForDirection(normal);
+ }
+ else
+ {
+ // Build tangent from bitangent.
+ bitangent = nv::normalize(bitangent, epsilon);
+
+ tangent = cross(bitangent, normal);
+ nvDebugCheck(isNormalized(tangent, epsilon));
+ }
+ }
+ else
+ {
+ tangent = nv::normalize(tangent, epsilon);
+#if 0
+ bitangent -= tangent * dot(tangent, bitangent);
+
+ if (lengthSquared(bitangent) < epsilon*epsilon)
+ {
+ bitangent = cross(tangent, normal);
+ nvDebugCheck(isNormalized(bitangent, epsilon));
+ }
+ else
+ {
+ bitangent = nv::normalize(bitangent, epsilon);
+ }
+#else
+ if (lengthSquared(bitangent) < epsilon*epsilon)
+ {
+ // Build bitangent from tangent.
+ bitangent = cross(tangent, normal);
+ nvDebugCheck(isNormalized(bitangent, epsilon));
+ }
+ else
+ {
+ bitangent = nv::normalize(bitangent, epsilon);
+
+ // At this point tangent and bitangent are orthogonal to normal, but we don't know whether their orientation.
+
+ Vector3 bisector;
+ if (lengthSquared(tangent + bitangent) < epsilon*epsilon)
+ {
+ bisector = tangent;
+ }
+ else
+ {
+ bisector = nv::normalize(tangent + bitangent);
+ }
+ Vector3 axis = nv::normalize(cross(bisector, normal));
+
+ //nvDebugCheck(isNormalized(axis, epsilon));
+ nvDebugCheck(equal(dot(axis, tangent), -dot(axis, bitangent), epsilon));
+
+ if (dot(axis, tangent) > 0)
+ {
+ tangent = bisector + axis;
+ bitangent = bisector - axis;
+ }
+ else
+ {
+ tangent = bisector - axis;
+ bitangent = bisector + axis;
+ }
+
+ // Make sure the resulting tangents are still perpendicular to the normal.
+ tangent -= normal * dot(normal, tangent);
+ bitangent -= normal * dot(normal, bitangent);
+
+ // Double check.
+ nvDebugCheck(equal(dot(normal, tangent), 0.0f, epsilon));
+ nvDebugCheck(equal(dot(normal, bitangent), 0.0f, epsilon));
+
+ // Normalize.
+ tangent = nv::normalize(tangent);
+ bitangent = nv::normalize(bitangent);
+
+ // If tangent and bitangent are not orthogonal, then derive bitangent from tangent, just in case...
+ if (!equal(dot(tangent, bitangent), 0.0f, epsilon)) {
+ bitangent = cross(tangent, normal);
+ bitangent = nv::normalize(bitangent);
+ }
+ }
+#endif
+ }
+
+ /*// Check vector lengths.
+ if (!isNormalized(normal, epsilon))
+ {
+ nvDebug("%f %f %f\n", normal.x, normal.y, normal.z);
+ nvDebug("%f %f %f\n", tangent.x, tangent.y, tangent.z);
+ nvDebug("%f %f %f\n", bitangent.x, bitangent.y, bitangent.z);
+ }*/
+
+ nvDebugCheck(isNormalized(normal, epsilon));
+ nvDebugCheck(isNormalized(tangent, epsilon));
+ nvDebugCheck(isNormalized(bitangent, epsilon));
+
+ // Check vector angles.
+ nvDebugCheck(equal(dot(normal, tangent), 0.0f, epsilon));
+ nvDebugCheck(equal(dot(normal, bitangent), 0.0f, epsilon));
+ nvDebugCheck(equal(dot(tangent, bitangent), 0.0f, epsilon));
+
+ // Check vector orientation.
+ const float det = dot(cross(normal, tangent), bitangent);
+ nvDebugCheck(equal(det, 1.0f, epsilon) || equal(det, -1.0f, epsilon));
+}
+
+
+/// Build an arbitrary frame for the given direction.
+void Basis::buildFrameForDirection(Vector3::Arg d, float angle/*= 0*/)
+{
+ nvCheck(isNormalized(d));
+ normal = d;
+
+ // Choose minimum axis.
+ if (fabsf(normal.x) < fabsf(normal.y) && fabsf(normal.x) < fabsf(normal.z))
+ {
+ tangent = Vector3(1, 0, 0);
+ }
+ else if (fabsf(normal.y) < fabsf(normal.z))
+ {
+ tangent = Vector3(0, 1, 0);
+ }
+ else
+ {
+ tangent = Vector3(0, 0, 1);
+ }
+
+ // Ortogonalize
+ tangent -= normal * dot(normal, tangent);
+ tangent = ::normalize(tangent);
+
+ bitangent = cross(normal, tangent);
+
+ // Rotate frame around normal according to angle.
+ if (angle != 0.0f) {
+ float c = cosf(angle);
+ float s = sinf(angle);
+ Vector3 tmp = c * tangent - s * bitangent;
+ bitangent = s * tangent + c * bitangent;
+ tangent = tmp;
+ }
+}
+
+bool Basis::isValid() const
+{
+ if (equal(normal, Vector3(0.0f))) return false;
+ if (equal(tangent, Vector3(0.0f))) return false;
+ if (equal(bitangent, Vector3(0.0f))) return false;
+
+ if (equal(determinant(), 0.0f)) return false;
+
+ return true;
+}
+
+
+/// Transform by this basis. (From this basis to object space).
+Vector3 Basis::transform(Vector3::Arg v) const
+{
+ Vector3 o = tangent * v.x;
+ o += bitangent * v.y;
+ o += normal * v.z;
+ return o;
+}
+
+/// Transform by the transpose. (From object space to this basis).
+Vector3 Basis::transformT(Vector3::Arg v)
+{
+ return Vector3(dot(tangent, v), dot(bitangent, v), dot(normal, v));
+}
+
+/// Transform by the inverse. (From object space to this basis).
+/// @note Uses Cramer's rule so the inverse is not accurate if the basis is ill-conditioned.
+Vector3 Basis::transformI(Vector3::Arg v) const
+{
+ const float det = determinant();
+ nvDebugCheck(!equal(det, 0.0f, 0.0f));
+
+ const float idet = 1.0f / det;
+
+ // Rows of the inverse matrix.
+ Vector3 r0(
+ (bitangent.y * normal.z - bitangent.z * normal.y),
+ -(bitangent.x * normal.z - bitangent.z * normal.x),
+ (bitangent.x * normal.y - bitangent.y * normal.x));
+
+ Vector3 r1(
+ -(tangent.y * normal.z - tangent.z * normal.y),
+ (tangent.x * normal.z - tangent.z * normal.x),
+ -(tangent.x * normal.y - tangent.y * normal.x));
+
+ Vector3 r2(
+ (tangent.y * bitangent.z - tangent.z * bitangent.y),
+ -(tangent.x * bitangent.z - tangent.z * bitangent.x),
+ (tangent.x * bitangent.y - tangent.y * bitangent.x));
+
+ return Vector3(dot(v, r0), dot(v, r1), dot(v, r2)) * idet;
+}
+
+
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