OpenRaider/src/MatMath.cpp

/*!
 *
 * \file src/MatMath.cpp
 * \brief Vector and Matrix math
 *
 * \author Mongoose
 */

#include <stdlib.h>
#include <math.h>
#include <float.h>

#include <MatMath.h>
#include <Vector3d.h>
#include <Matrix.h>

bool equalEpsilon(vec_t a, vec_t b) {
    vec_t epsilon = FLT_EPSILON;
    if (fabs(a - b) <= (((fabs(b) > fabs(a)) ? fabs(b) : fabs(a)) * epsilon))
        return true;
    return false;
}

vec_t helIntersectionOfAbstractSpheres(vec3_t centerA, vec_t radiusA,
        vec3_t centerB, vec_t radiusB)
{
    Vector3d a = Vector3d(centerA);
    Vector3d b = Vector3d(centerB);
    Vector3d d = a - b;
    vec_t dist, minDist;

    dist = Vector3d::dot(d, d);
    minDist = radiusA + radiusB;

    return (dist <= minDist * minDist);
}


inline vec_t square(vec_t a)
{
    return a * a;
}


// Returns number of intersections and intersection position(s)
// Got algorithm from http://astronomy.swin.edu.au/~pbourke/geometry/
int helIntersectionOfAbstractSphereAndLine(vec3_t center, vec_t radius,
        vec3_t posA, vec3_t posB,
        vec3_t intersectionA,
        vec3_t intersectionB)
{
    // float x , y , z;
    vec_t a, b, c, mu, i ;


    a = (square(posB[0] - posA[0]) +
            square(posB[1] - posA[1]) +
            square(posB[2] - posA[2]));
    b = (2 * ((posB[0] - posA[0]) * (posA[0] - center[0]) +
                (posB[1] - posA[1]) * (posA[1] - center[1]) +
                (posB[2] - posA[2]) * (posA[2] - center[2])));
    c = (square(center[0]) + square(center[1]) +
            square(center[2]) + square(posA[0]) +
            square(posA[1]) + square(posA[2]) -
            2 * (center[0]*posA[0] + center[1]*posA[1] + center[2]*posA[2]) -
            square(radius));

    i = b * b - 4 * a * c;


    if (i < 0.0)
    {
        // No intersection
        return 0;
    }
    else if (i == 0.0)
    {
        // One intersection
        mu = -b/(2*a) ;
        intersectionA[0] = posA[0] + mu*(posB[0]-posA[0]);
        intersectionA[1] = posA[1] + mu*(posB[1]-posA[1]);
        intersectionA[2] = posA[2] + mu*(posB[2]-posA[2]);

        return 1;
    }
    else
    {
        // Two intersections

        // First intersection
        mu = (-b + sqrtf( square(b) - 4.0f*a*c)) / (2.0f*a);
        intersectionA[0] = posA[0] + mu*(posB[0]-posA[0]);
        intersectionA[1] = posA[1] + mu*(posB[1]-posA[1]);
        intersectionA[2] = posA[2] + mu*(posB[2]-posA[2]);

        // Second intersection
        mu = (-b - sqrtf(square(b) - 4.0f*a*c)) / (2.0f*a);
        intersectionB[0] = posA[0] + mu*(posB[0]-posA[0]);
        intersectionB[1] = posA[1] + mu*(posB[1]-posA[1]);
        intersectionB[2] = posA[2] + mu*(posB[2]-posA[2]);

        return 2;
    }
}


int helIntersectionLineAndPolygon(vec3_t intersect,
        vec3_t p1, vec3_t p2,
        vec3_t *polygon)
{
    //  vec3_t normal, a, b;
    Vector3d a, b, normal, pA, pB;
    vec_t d, denominator, mu;
    double theta;


    pA = Vector3d(p1);
    pB = Vector3d(p2);

    // Find normal
    //mtkVectorSubtract(polygon[1], polygon[0], a);
    a = Vector3d(polygon[1]) - Vector3d(polygon[0]);
    //mtkVectorSubtract(polygon[2], polygon[0], b);
    b = Vector3d(polygon[2]) - Vector3d(polygon[0]);
    normal = Vector3d::cross(a, b);
    //mtkVectorCrossProduct(a, b, normal);
    normal.normalize();
    //mtkVectorNormalize(normal, normal);

    // find D
    //d = (normal[0] * polygon[0][0] -
    //    normal[1] * polygon[0][1] -
    //    normal[2] * polygon[0][2]);
    d = (normal.mVec[0] * polygon[0][0] -
            normal.mVec[1] * polygon[0][1] -
            normal.mVec[2] * polygon[0][2]);

    // line segment parallel to plane?
    //mtkVectorSubtract(p2, p1, a); // cache p2 - p1 => a
    a = pB - pA;

    //denominator = (normal[0] * a[0] +
    //                  normal[1] * a[1] +
    //                  normal[2] * a[2]);
    denominator = Vector3d::dot(normal, a);

    if (denominator > 0.0)
        return 0;

    // Line segment contains intercept point?
    //mu = - ((d + normal[0] * p1[0] + normal[1] * p1[1] + normal[2] * p1[2]) /
    //        denominator);
    mu = -((d + Vector3d::dot(normal, pA)) / denominator);

    if (mu < 0.0 || mu > 1.0)
        return 0;

    //intersect[0] = p1[0] + mu * a[0];
    //intersect[1] = p1[1] + mu * a[1];
    //intersect[2] = p1[2] + mu * a[2];
    b = pA + (a * mu);
    intersect[0] = b.mVec[0];
    intersect[1] = b.mVec[1];
    intersect[2] = b.mVec[2];


    // See if the intercept is bound by polygon by winding number
#ifdef WINDING_NUMBERS_TRIANGLE
    mtkVectorSubtract(polygon[0], intersect, a);
    mtkVectorNormalize(a, a);
    mtkVectorSubtract(polygon[1], intersect, b);
    mtkVectorNormalize(b, b);
    mtkVectorSubtract(polygon[2], intersect, c);
    mtkVectorNormalize(c, c);

    t0 = mtkVectorDotProduct(a, b);
    t1 = mtkVectorDotProduct(b, c);
    t2 = mtkVectorDotProduct(c, a);

    total = HEL_RAD_TO_DEG(acos(t0) + acos(t1) + acos(t2));

    if (total - 360 < 0.0)
        return 0;
#else // assume convex polygons here for sure
    //mtkVectorSubtract(intersect, polygon[0], a);
    //theta = mtkVectorDotProduct(a, normal);
    theta = Vector3d::dot(b - Vector3d(polygon[0]), normal); // b = intersect

    if (theta >= 90.0) // Yeah I know
        return 0;
#endif

    return 1;
}


vec_t helDistToSphereFromPlane3v(vec3_t center, vec_t radius, vec4_t plane)
{
    vec_t d;


    d = (plane[0] * center[0] +
            plane[1] * center[1] +
            plane[2] * center[2] +
            plane[3]);

    if (d <= -radius)
        return 0;

    return d + radius;
}


vec_t helDistToBboxFromPlane3v(vec3_t min, vec3_t max, vec4_t plane)
{
    vec3_t center;
    vec_t d, radius;


    helMidpoint3v(min, max, center);

    d = (plane[0] * center[0] +
            plane[1] * center[1] +
            plane[2] * center[2] +
            plane[3]);

    radius = helDist3v(max, center);

    if (d <= -radius)
        return 0;

    return d + radius;
}


vec_t helDist3v(vec3_t a, vec3_t b)
{
    return (sqrtf( ((b[0] - a[0]) * (b[0] - a[0])) +
                ((b[1] - a[1]) * (b[1] - a[1])) +
                ((b[2] - a[2]) * (b[2] - a[2]))));
}


void helMidpoint3v(vec3_t a, vec3_t b, vec3_t mid)
{
    mid[0] = (a[0] + b[0]) / 2.0f;
    mid[1] = (a[1] + b[1]) / 2.0f;
    mid[2] = (a[2] + b[2]) / 2.0f;
}


vec_t helNorm4v(vec4_t v)
{
    return (sqrtf(v[0]*v[0] + v[1]*v[1] + v[2]*v[2] + v[3]*v[3]));
}


vec_t helNorm3v(vec3_t v)
{
    return (sqrtf(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]));
}


vec_t helNorm2v(vec2_t v)
{
    return (sqrtf(v[0]*v[0] + v[1]*v[1]));
}


vec_t helRandomNum(vec_t from, vec_t to)
{
    return from + ((to - from) * rand() / (RAND_MAX + 1.0f));
}