godot/thirdparty/thekla_atlas/nvmesh/param/ParameterizationQuality.cpp

// Copyright NVIDIA Corporation 2008 -- Ignacio Castano <icastano@nvidia.com>

#include "nvmesh.h" // pch

#include "ParameterizationQuality.h"

#include "nvmesh/halfedge/Mesh.h"
#include "nvmesh/halfedge/Face.h"
#include "nvmesh/halfedge/Vertex.h"
#include "nvmesh/halfedge/Edge.h"

#include "nvmath/Vector.inl"

#include "nvcore/Debug.h"

#include <float.h>


using namespace nv;

#if 0
/*
float triangleConformalEnergy(Vector3 q[3], Vector2 p[3])
{
const Vector3 v1 = q[0];
const Vector3 v2 = q[1];
const Vector3 v3 = q[2];

const Vector2 w1 = p[0];
const Vector2 w2 = p[1];
const Vector2 w3 = p[2];

float x1 = v2.x() - v1.x();
float x2 = v3.x() - v1.x();
float y1 = v2.y() - v1.y();
float y2 = v3.y() - v1.y();
float z1 = v2.z() - v1.z();
float z2 = v3.z() - v1.z();

float s1 = w2.x() - w1.x();
float s2 = w3.x() - w1.x();
float t1 = w2.y() - w1.y();
float t2 = w3.y() - w1.y();

float r = 1.0f / (s1 * t2 - s2 * t1);
Vector3 sdir((t2 * x1 - t1 * x2) * r, (t2 * y1 - t1 * y2) * r, (t2 * z1 - t1 * z2) * r);
Vector3 tdir((s1 * x2 - s2 * x1) * r, (s1 * y2 - s2 * y1) * r, (s1 * z2 - s2 * z1) * r);

Vector3 N = cross(v3-v1, v2-v1);

// Rotate 90 around N.
}
*/

static float triangleConformalEnergy(Vector3 q[3], Vector2 p[3])
{
    // Using Denis formulas:
    Vector3 c0 = q[1] - q[2];
    Vector3 c1 = q[2] - q[0];
    Vector3 c2 = q[0] - q[1];

    Vector3 N = cross(-c0, c1);
    float T = length(N);	// 2T
    N = normalize(N, 0);

    float cot_alpha0 = dot(-c1, c2) / length(cross(-c1, c2));
    float cot_alpha1 = dot(-c2, c0) / length(cross(-c2, c0));
    float cot_alpha2 = dot(-c0, c1) / length(cross(-c0, c1));

    Vector3 t0 = -cot_alpha1 * c1 + cot_alpha2 * c2;
    Vector3 t1 = -cot_alpha2 * c2 + cot_alpha0 * c0;
    Vector3 t2 = -cot_alpha0 * c0 + cot_alpha1 * c1;

    nvCheck(equal(length(t0), length(c0)));
    nvCheck(equal(length(t1), length(c1)));
    nvCheck(equal(length(t2), length(c2)));
    nvCheck(equal(dot(t0, c0), 0));
    nvCheck(equal(dot(t1, c1), 0));
    nvCheck(equal(dot(t2, c2), 0));

    // Gradients
    Vector3 grad_u = 1.0f / T * (p[0].x * t0 + p[1].x * t1 + p[2].x * t2);
    Vector3 grad_v = 1.0f / T * (p[0].y * t0 + p[1].y * t1 + p[2].y * t2);

    // Rotated gradients
    Vector3 Jgrad_u = 1.0f / T * (p[0].x * c0 + p[1].x * c1 + p[2].x * c2);
    Vector3 Jgrad_v = 1.0f / T * (p[0].y * c0 + p[1].y * c1 + p[2].y * c2);

    // Using Lengyel's formulas:
    { 
        const Vector3 v1 = q[0];
        const Vector3 v2 = q[1];
        const Vector3 v3 = q[2];

        const Vector2 w1 = p[0];
        const Vector2 w2 = p[1];
        const Vector2 w3 = p[2];

        float x1 = v2.x - v1.x;
        float x2 = v3.x - v1.x;
        float y1 = v2.y - v1.y;
        float y2 = v3.y - v1.y;
        float z1 = v2.z - v1.z;
        float z2 = v3.z - v1.z;

        float s1 = w2.x - w1.x;
        float s2 = w3.x - w1.x;
        float t1 = w2.y - w1.y;
        float t2 = w3.y - w1.y;

        float r = 1.0f / (s1 * t2 - s2 * t1);
        Vector3 sdir((t2 * x1 - t1 * x2) * r, (t2 * y1 - t1 * y2) * r, (t2 * z1 - t1 * z2) * r);
        Vector3 tdir((s1 * x2 - s2 * x1) * r, (s1 * y2 - s2 * y1) * r, (s1 * z2 - s2 * z1) * r);

        Vector3 Jsdir = cross(N, sdir);
        Vector3 Jtdir = cross(N, tdir);

        float x = 3;
    }

    // check: sdir == grad_u
    // check: tdir == grad_v

    return length(grad_u - Jgrad_v);
}
#endif // 0


ParameterizationQuality::ParameterizationQuality()
{
    m_totalTriangleCount = 0;
    m_flippedTriangleCount = 0;
    m_zeroAreaTriangleCount = 0;

    m_parametricArea = 0.0f;
    m_geometricArea = 0.0f;

    m_stretchMetric = 0.0f;
    m_maxStretchMetric = 0.0f;

    m_conformalMetric = 0.0f;
    m_authalicMetric = 0.0f;
}

ParameterizationQuality::ParameterizationQuality(const HalfEdge::Mesh * mesh)
{
    nvDebugCheck(mesh != NULL);

    m_totalTriangleCount = 0;
    m_flippedTriangleCount = 0;
    m_zeroAreaTriangleCount = 0;

    m_parametricArea = 0.0f;
    m_geometricArea = 0.0f;

    m_stretchMetric = 0.0f;
    m_maxStretchMetric = 0.0f;

    m_conformalMetric = 0.0f;
    m_authalicMetric = 0.0f;

    const uint faceCount = mesh->faceCount();
    for (uint f = 0; f < faceCount; f++)
    {
        const HalfEdge::Face * face = mesh->faceAt(f);
        const HalfEdge::Vertex * vertex0 = NULL;

        Vector3 p[3];
        Vector2 t[3];

        for (HalfEdge::Face::ConstEdgeIterator it(face->edges()); !it.isDone(); it.advance())
        {
            const HalfEdge::Edge * edge = it.current();

            if (vertex0 == NULL)
            {
                vertex0 = edge->vertex;

                p[0] = vertex0->pos;
                t[0] = vertex0->tex;
            }
            else if (edge->to() != vertex0)
            {
                p[1] = edge->from()->pos;
                p[2] = edge->to()->pos;
                t[1] = edge->from()->tex;
                t[2] = edge->to()->tex;

                processTriangle(p, t);
            }
        }
    }

    if (m_flippedTriangleCount + m_zeroAreaTriangleCount == faceCount)
    {
        // If all triangles are flipped, then none is.
        m_flippedTriangleCount = 0;
    }

    nvDebugCheck(isFinite(m_parametricArea) && m_parametricArea >= 0);
    nvDebugCheck(isFinite(m_geometricArea) && m_geometricArea >= 0);
    nvDebugCheck(isFinite(m_stretchMetric));
    nvDebugCheck(isFinite(m_maxStretchMetric));
    nvDebugCheck(isFinite(m_conformalMetric));
    nvDebugCheck(isFinite(m_authalicMetric));
}

bool ParameterizationQuality::isValid() const
{
    return m_flippedTriangleCount == 0; // @@ Does not test for self-overlaps.
}

float ParameterizationQuality::rmsStretchMetric() const
{
    if (m_geometricArea == 0) return 0.0f;
    float normFactor = sqrtf(m_parametricArea / m_geometricArea);
    return sqrtf(m_stretchMetric / m_geometricArea) * normFactor;
}

float ParameterizationQuality::maxStretchMetric() const
{
    if (m_geometricArea == 0) return 0.0f;
    float normFactor = sqrtf(m_parametricArea / m_geometricArea);
    return m_maxStretchMetric * normFactor;
}

float ParameterizationQuality::rmsConformalMetric() const
{
    if (m_geometricArea == 0) return 0.0f;
    return sqrtf(m_conformalMetric / m_geometricArea);
}

float ParameterizationQuality::maxAuthalicMetric() const
{
    if (m_geometricArea == 0) return 0.0f;
    return sqrtf(m_authalicMetric / m_geometricArea);
}

void ParameterizationQuality::operator += (const ParameterizationQuality & pq)
{
    m_totalTriangleCount += pq.m_totalTriangleCount;
    m_flippedTriangleCount += pq.m_flippedTriangleCount;
    m_zeroAreaTriangleCount += pq.m_zeroAreaTriangleCount;

    m_parametricArea += pq.m_parametricArea;
    m_geometricArea += pq.m_geometricArea;

    m_stretchMetric += pq.m_stretchMetric;
    m_maxStretchMetric = max(m_maxStretchMetric, pq.m_maxStretchMetric);

    m_conformalMetric += pq.m_conformalMetric;
    m_authalicMetric += pq.m_authalicMetric;
}


void ParameterizationQuality::processTriangle(Vector3 q[3], Vector2 p[3])
{
    m_totalTriangleCount++;

    // Evaluate texture stretch metric. See:
    // - "Texture Mapping Progressive Meshes", Sander, Snyder, Gortler & Hoppe
    // - "Mesh Parameterization: Theory and Practice", Siggraph'07 Course Notes, Hormann, Levy & Sheffer.

    float t1 = p[0].x;
    float s1 = p[0].y;
    float t2 = p[1].x;
    float s2 = p[1].y;
    float t3 = p[2].x;
    float s3 = p[2].y;

    float geometricArea = length(cross(q[1] - q[0], q[2] - q[0])) / 2;
    float parametricArea = ((s2 - s1)*(t3 - t1) - (s3 - s1)*(t2 - t1)) / 2;
    
    if (isZero(parametricArea))
    {
        m_zeroAreaTriangleCount++;
        return;
    }

    Vector3 Ss = (q[0] * (t2- t3) + q[1] * (t3 - t1) + q[2] * (t1 - t2)) / (2 * parametricArea);
    Vector3 St = (q[0] * (s3- s2) + q[1] * (s1 - s3) + q[2] * (s2 - s1)) / (2 * parametricArea);

    float a = dot(Ss, Ss); // E
    float b = dot(Ss, St); // F
    float c = dot(St, St); // G

    // Compute eigen-values of the first fundamental form:
    float sigma1 = sqrtf(0.5f * max(0.0f, a + c - sqrtf(square(a - c) + 4 * square(b)))); // gamma uppercase, min eigenvalue.
    float sigma2 = sqrtf(0.5f * max(0.0f, a + c + sqrtf(square(a - c) + 4 * square(b)))); // gamma lowercase, max eigenvalue.
    nvCheck(sigma2 >= sigma1);

    // isometric: sigma1 = sigma2 = 1
    // conformal: sigma1 / sigma2 = 1
    // authalic: sigma1 * sigma2 = 1

    float rmsStretch = sqrtf((a + c) * 0.5f);
    float rmsStretch2 = sqrtf((square(sigma1) + square(sigma2)) * 0.5f);
    nvDebugCheck(equal(rmsStretch, rmsStretch2, 0.01f));

    if (parametricArea < 0.0f)
    {
        // Count flipped triangles.
        m_flippedTriangleCount++;

        parametricArea = fabsf(parametricArea);
    }

    m_stretchMetric += square(rmsStretch) * geometricArea;
    m_maxStretchMetric = max(m_maxStretchMetric, sigma2);

    if (!isZero(sigma1, 0.000001f)) {
        // sigma1 is zero when geometricArea is zero.
        m_conformalMetric += (sigma2 / sigma1) * geometricArea;
    }
    m_authalicMetric += (sigma1 * sigma2) * geometricArea;

    // Accumulate total areas.
    m_geometricArea += geometricArea;
    m_parametricArea += parametricArea;


    //triangleConformalEnergy(q, p);
}