/*  Starshatter: The Open Source Project
    Copyright (c) 2021-2024, Starshatter: The Open Source Project Contributors
    Copyright (c) 2011-2012, Starshatter OpenSource Distribution Contributors
    Copyright (c) 1997-2006, Destroyer Studios LLC.

    AUTHOR:       John DiCamillo


    OVERVIEW
    ========
    Geometric Utilities
*/

#include "Geometry.h"

// +--------------------------------------------------------------------+

void Rect::Inflate(int dx, int dy)
{
    x -= dx;
    w += dx*2;
    y -= dy;
    h += dy*2;
}

void Rect::Deflate(int dx, int dy)
{
    x += dx;
    w -= dx*2;
    y += dy;
    h -= dy*2;
}

void Rect::Inset(int l, int r, int t, int b)
{
    x += l;
    y += t;
    w -= l + r;
    h -= t + b;
}

int Rect::Contains(int ax, int ay) const
{
    if (ax < x)    return 0;
    if (ax > x+w)  return 0;
    if (ay < y)    return 0;
    if (ay > y+h)  return 0;

    return 1;
}

// +--------------------------------------------------------------------+

double
Point::Normalize()
{
    double scale = 1.0;
    double len   = length();

    if (len)
    scale /= len;

    x *= scale;
    y *= scale;
    z *= scale;

    return len;
}

// +--------------------------------------------------------------------+

void
Point::SetElement(int i, double v)
{
    switch (i) {
    case 0:  x = v; break;
    case 1:  y = v; break;
    case 2:  z = v; break;
    default:        break;
    }
}

// +--------------------------------------------------------------------+

Point
Point::operator*(const Matrix& m) const
{
    Point result;

    result.x = (m.elem[0][0] * x) + (m.elem[1][0] * y) + (m.elem[2][0] * z);
    result.y = (m.elem[0][1] * x) + (m.elem[1][1] * y) + (m.elem[2][1] * z);
    result.z = (m.elem[0][2] * x) + (m.elem[1][2] * y) + (m.elem[2][2] * z);

    return result;
}

// +--------------------------------------------------------------------+

double ClosestApproachTime(const Point& loc1, const Point& vel1,
const Point& loc2, const Point& vel2)
{
    double t = 0;

    Point D  = loc1-loc2;
    Point Dv = vel1-vel2;

    if (Dv.x || Dv.y || Dv.z)
    t = -1 * (Dv*D) / (Dv*Dv);

    return t;
}

// +--------------------------------------------------------------------+

float
Vec2::Normalize()
{
    float  scale = 1.0f;
    float  len   = length();

    if (len)
    scale /= len;

    x *= scale;
    y *= scale;

    return len;
}

// +--------------------------------------------------------------------+

float
Vec3::Normalize()
{
    float  scale = 1.0f;
    float  len   = length();

    if (len)
    scale /= len;

    x *= scale;
    y *= scale;
    z *= scale;

    return len;
}

// +--------------------------------------------------------------------+

Vec3
Vec3::operator*(const Matrix& m) const
{
    Vec3 result;

    result.x = (float) ((m.elem[0][0] * x) + (m.elem[1][0] * y) + (m.elem[2][0] * z));
    result.y = (float) ((m.elem[0][1] * x) + (m.elem[1][1] * y) + (m.elem[2][1] * z));
    result.z = (float) ((m.elem[0][2] * x) + (m.elem[1][2] * y) + (m.elem[2][2] * z));

    return result;
}

// +--------------------------------------------------------------------+

double ClosestApproachTime(const Vec3& loc1, const Vec3& vel1,
const Vec3& loc2, const Vec3& vel2)
{
    double t = 0;

    Point D  = loc1-loc2;
    Point Dv = vel1-vel2;

    if (Dv.x || Dv.y || Dv.z)
    t = -1 * (Dv*D) / (Dv*Dv);

    return t;
}

// +--------------------------------------------------------------------+

double
Quaternion::Normalize()
{
    double scale = 1.0;
    double len   = length();

    if (len)
    scale /= len;

    x *= scale;
    y *= scale;
    z *= scale;
    w *= scale;

    return len;
}

// +--------------------------------------------------------------------+

Matrix::Matrix()
{
    Identity();
}

Matrix::Matrix(const Matrix& m)
{
    CopyMemory(elem, m.elem, sizeof(elem));
}

Matrix::Matrix(const Point& vrt, const Point& vup, const Point& vpn)
{
    elem[0][0] = vrt.x;
    elem[0][1] = vrt.y;
    elem[0][2] = vrt.z;

    elem[1][0] = vup.x;
    elem[1][1] = vup.y;
    elem[1][2] = vup.z;

    elem[2][0] = vpn.x;
    elem[2][1] = vpn.y;
    elem[2][2] = vpn.z;
}

// +--------------------------------------------------------------------+

Matrix&
Matrix::operator =(const Matrix& m)
{
    CopyMemory(elem, m.elem, sizeof(elem));

    return *this;
}

// +--------------------------------------------------------------------+

Matrix&
Matrix::operator*=(const Matrix& m)
{
    return *this = *this * m;
}

// +--------------------------------------------------------------------+

void
Matrix::Identity()
{
    elem[0][0] = 1;
    elem[0][1] = 0;
    elem[0][2] = 0;

    elem[1][0] = 0;
    elem[1][1] = 1;
    elem[1][2] = 0;

    elem[2][0] = 0;
    elem[2][1] = 0;
    elem[2][2] = 1;
}

// +--------------------------------------------------------------------+

inline void swap_elem(double& a, double& b) { double t=a; a=b; b=t; }

void
Matrix::Transpose()
{
    swap_elem(elem[0][1], elem[1][0]);
    swap_elem(elem[0][2], elem[2][0]);
    swap_elem(elem[1][2], elem[2][1]);
}

// +--------------------------------------------------------------------+

void
Matrix::Rotate(double roll, double pitch, double yaw)
{
    double e[3][3];
    CopyMemory(e, elem, sizeof(elem));

    double sr = sin(roll);
    double cr = cos(roll);
    double sp = sin(pitch);
    double cp = cos(pitch);
    double sy = sin(yaw);
    double cy = cos(yaw);

    double a,b,c;

    a = cy*cr;
    b = cy*sr;
    c = -sy;

    elem[0][0] = a*e[0][0] + b*e[1][0] + c*e[2][0];
    elem[0][1] = a*e[0][1] + b*e[1][1] + c*e[2][1];
    elem[0][2] = a*e[0][2] + b*e[1][2] + c*e[2][2];

    a = cp*-sr + sp*sy*cr;
    b = cp* cr + sp*sy*sr;
    c = sp*cy;

    elem[1][0] = a*e[0][0] + b*e[1][0] + c*e[2][0];
    elem[1][1] = a*e[0][1] + b*e[1][1] + c*e[2][1];
    elem[1][2] = a*e[0][2] + b*e[1][2] + c*e[2][2];

    a = -sp*-sr + cp*sy*cr;
    b = -sp* cr + cp*sy*sr;
    c = cp*cy;

    elem[2][0] = a*e[0][0] + b*e[1][0] + c*e[2][0];
    elem[2][1] = a*e[0][1] + b*e[1][1] + c*e[2][1];
    elem[2][2] = a*e[0][2] + b*e[1][2] + c*e[2][2];
}

// +--------------------------------------------------------------------+

void
Matrix::Roll(double roll)
{
    double s = sin(roll);
    double c = cos(roll);

    double e00 = elem[0][0];
    double e01 = elem[0][1];
    double e02 = elem[0][2];
    double e10 = elem[1][0];
    double e11 = elem[1][1];
    double e12 = elem[1][2];

    elem[0][0] =  c*e00 + s*e10;
    elem[0][1] =  c*e01 + s*e11;
    elem[0][2] =  c*e02 + s*e12;

    elem[1][0] = -s*e00 + c*e10;
    elem[1][1] = -s*e01 + c*e11;
    elem[1][2] = -s*e02 + c*e12;
}

// +--------------------------------------------------------------------+

void
Matrix::Pitch(double pitch)
{
    double s = sin(pitch);
    double c = cos(pitch);

    double e10 = elem[1][0];
    double e11 = elem[1][1];
    double e12 = elem[1][2];
    double e20 = elem[2][0];
    double e21 = elem[2][1];
    double e22 = elem[2][2];

    elem[1][0] =  c*e10 + s*e20;
    elem[1][1] =  c*e11 + s*e21;
    elem[1][2] =  c*e12 + s*e22;

    elem[2][0] = -s*e10 + c*e20;
    elem[2][1] = -s*e11 + c*e21;
    elem[2][2] = -s*e12 + c*e22;
}

// +--------------------------------------------------------------------+

void
Matrix::Yaw(double yaw)
{
    double s = sin(yaw);
    double c = cos(yaw);

    double e00 = elem[0][0];
    double e01 = elem[0][1];
    double e02 = elem[0][2];
    double e20 = elem[2][0];
    double e21 = elem[2][1];
    double e22 = elem[2][2];

    elem[0][0] = c*e00 - s*e20;
    elem[0][1] = c*e01 - s*e21;
    elem[0][2] = c*e02 - s*e22;

    elem[2][0] = s*e00 + c*e20;
    elem[2][1] = s*e01 + c*e21;
    elem[2][2] = s*e02 + c*e22;
}

// +--------------------------------------------------------------------+

inline int sign(double d) { return (d >= 0); }

void
Matrix::ComputeEulerAngles(double& roll, double& pitch, double& yaw) const
{
    double cy;

    yaw   = asin(-elem[0][2]);
    cy    = cos(yaw);
    roll  = asin(elem[0][1] / cy);
    pitch = asin(elem[1][2] / cy);

    if (sign(cos(roll)*cy) != sign(elem[0][0]))
    roll = PI - roll;

    if (sign(cos(pitch)*cy) != sign(elem[2][2]))
    pitch = PI - pitch;
}

// +--------------------------------------------------------------------+

Matrix
Matrix::operator*(const Matrix& m) const
{
    Matrix r;

    r.elem[0][0] = elem[0][0]*m.elem[0][0] + elem[0][1]*m.elem[1][0] + elem[0][2]*m.elem[2][0];
    r.elem[0][1] = elem[0][0]*m.elem[0][1] + elem[0][1]*m.elem[1][1] + elem[0][2]*m.elem[2][1];
    r.elem[0][2] = elem[0][0]*m.elem[0][2] + elem[0][1]*m.elem[1][2] + elem[0][2]*m.elem[2][2];

    r.elem[1][0] = elem[1][0]*m.elem[0][0] + elem[1][1]*m.elem[1][0] + elem[1][2]*m.elem[2][0];
    r.elem[1][1] = elem[1][0]*m.elem[0][1] + elem[1][1]*m.elem[1][1] + elem[1][2]*m.elem[2][1];
    r.elem[1][2] = elem[1][0]*m.elem[0][2] + elem[1][1]*m.elem[1][2] + elem[1][2]*m.elem[2][2];

    r.elem[2][0] = elem[2][0]*m.elem[0][0] + elem[2][1]*m.elem[1][0] + elem[2][2]*m.elem[2][0];
    r.elem[2][1] = elem[2][0]*m.elem[0][1] + elem[2][1]*m.elem[1][1] + elem[2][2]*m.elem[2][1];
    r.elem[2][2] = elem[2][0]*m.elem[0][2] + elem[2][1]*m.elem[1][2] + elem[2][2]*m.elem[2][2];

    return r;
}

// +--------------------------------------------------------------------+

Point
Matrix::operator*(const Point& p) const
{
    Point result;

    result.x = (elem[0][0] * p.x) + (elem[0][1] * p.y) + (elem[0][2] * p.z);
    result.y = (elem[1][0] * p.x) + (elem[1][1] * p.y) + (elem[1][2] * p.z);
    result.z = (elem[2][0] * p.x) + (elem[2][1] * p.y) + (elem[2][2] * p.z);

    return result;
}

// +--------------------------------------------------------------------+

Vec3
Matrix::operator*(const Vec3& v) const
{
    Vec3 result;

    result.x = (float) ((elem[0][0] * v.x) + (elem[0][1] * v.y) + (elem[0][2] * v.z));
    result.y = (float) ((elem[1][0] * v.x) + (elem[1][1] * v.y) + (elem[1][2] * v.z));
    result.z = (float) ((elem[2][0] * v.x) + (elem[2][1] * v.y) + (elem[2][2] * v.z));

    return result;
}

// +--------------------------------------------------------------------+

double
Matrix::Cofactor(int i, int j) const
{
    int i1=0;
    int i2=2;
    int j1=0;
    int j2=2;

    if (i==0) i1=1; else if (i==2) i2=1;
    if (j==0) j1=1; else if (j==2) j2=1;

    double factor = elem[i1][j1]*elem[i2][j2] - elem[i1][j2]*elem[i2][j1];

    if ((i+j) & 1)
    factor *= -1;

    return factor;
}

// +--------------------------------------------------------------------+

void
Matrix::Invert()
{
    double f[3][3];
    int    i, j;

    for (i = 0; i < 3; i++)
    for (j = 0; j < 3; j++)
    f[i][j] = Cofactor(j,i);

    double det = elem[0][0] * f[0][0] +
    elem[0][1] * f[1][0] +
    elem[0][2] * f[2][0];

    if (det != 0) {
        double inv = 1/det;

        for (i = 0; i < 3; i++)
        for (j = 0; j < 3; j++)
        elem[i][j] = f[i][j] * inv;
    }
}

// +--------------------------------------------------------------------+
// +--------------------------------------------------------------------+
// +--------------------------------------------------------------------+

Plane::Plane()
: distance(0.0f)
{ }

Plane::Plane(const Point& p0, const Point& p1, const Point& p2)
{
    Point d1 = p1 - p0;
    Point d2 = p2 - p0;

    normal = (Vec3) d1.cross(d2);
    normal.Normalize();

    distance = (float) (normal * p0);
}

Plane::Plane(const Vec3& v0, const Vec3& v1, const Vec3& v2)
{
    Vec3 d1 = v1 - v0;
    Vec3 d2 = v2 - v0;

    normal = d1.cross(d2);
    normal.Normalize();

    distance = normal * v0;
}

void Plane::Rotate(const Vec3& v0, const Matrix& m)
{
    normal   = normal * m;
    distance = normal * v0;
}

void Plane::Translate(const Vec3& v0)
{
    distance = normal * v0;
}

// +--------------------------------------------------------------------+
// 3-D dot product.

double DotProduct(const Point& a, const Point& b)
{
    return (a.x * b.x) + (a.y * b.y) + (a.z * b.z);
}

// +--------------------------------------------------------------------+
// 3-D cross product.

void CrossProduct(const Point& a, const Point& b, Point& out)
{
    out.x = (a.y * b.z) - (a.z * b.y);
    out.y = (a.z * b.x) - (a.x * b.z);
    out.z = (a.x * b.y) - (a.y * b.x);
}

// +--------------------------------------------------------------------+
// Concatenate two 3x3 matrices.

void MConcat(double in1[3][3], double in2[3][3], double out[3][3])
{
    int     i, j;

    for (i=0 ; i<3 ; i++) {
        for (j=0 ; j<3 ; j++) {
            out[i][j] = in1[i][0] * in2[0][j] +
            in1[i][1] * in2[1][j] +
            in1[i][2] * in2[2][j];
        }
    }
}

/* GRAPHICS GEMS II ----------------------------------------------------
*
* lines_intersect:  AUTHOR: Mukesh Prasad
*
*   This function computes whether two line segments,
*   respectively joining the input points (x1,y1) -- (x2,y2)
*   and the input points (x3,y3) -- (x4,y4) intersect.
*   If the lines intersect, the output variables x, y are
*   set to coordinates of the point of intersection.
*
*   All values are in integers.  The returned value is rounded
*   to the nearest integer point.
*
*   If non-integral grid points are relevant, the function
*   can easily be transformed by substituting floating point
*   calculations instead of integer calculations.
*
*   Entry
*        x1, y1,  x2, y2   Coordinates of endpoints of one segment.
*        x3, y3,  x4, y4   Coordinates of endpoints of other segment.
*
*   Exit
*        x, y              Coordinates of intersection point.
*
*   The value returned by the function is one of:
*
*        DONT_INTERSECT    0
*        DO_INTERSECT      1
*        COLLINEAR         2
*
* Error conditions:
*
*     Depending upon the possible ranges, and particularly on 16-bit
*     computers, care should be taken to protect from overflow.
*
*     In the following code, 'long' values have been used for this
*     purpose, instead of 'int'.
*
*/

#define DONT_INTERSECT    0
#define DO_INTERSECT      1
#define COLLINEAR         2

inline int SAME_SIGNS(double a, double b)
{
    return ((a>=0 && b>=0) || (a<0 && b<0));
}

int
lines_intersect(
/* 1st line segment */ double x1, double y1, double x2, double y2,
/* 2nd line segment */ double x3, double y3, double x4, double y4,
/* pt of intersect  */ double& ix, double& iy)
{
    double a1, a2, b1, b2, c1, c2; /* Coefficients of line eqns. */
    double r1, r2, r3, r4;         /* 'Sign' values */
    double denom, offset, num;     /* Intermediate values */

    /* Compute a1, b1, c1, where line joining points 1 and 2
    * is "a1 x  +  b1 y  +  c1  =  0".  */

    a1 = y2 - y1;
    b1 = x1 - x2;
    c1 = x2 * y1 - x1 * y2;

    /* Compute r3 and r4.  */

    r3 = a1 * x3 + b1 * y3 + c1;
    r4 = a1 * x4 + b1 * y4 + c1;

    /* Check signs of r3 and r4.  If both point 3 and point 4 lie on
    * same side of line 1, the line segments do not intersect.  */

    if ( r3 != 0 &&
            r4 != 0 &&
            SAME_SIGNS( r3, r4 ))
    return ( DONT_INTERSECT );

    /* Compute a2, b2, c2 */

    a2 = y4 - y3;
    b2 = x3 - x4;
    c2 = x4 * y3 - x3 * y4;

    /* Compute r1 and r2 */

    r1 = a2 * x1 + b2 * y1 + c2;
    r2 = a2 * x2 + b2 * y2 + c2;

    /* Check signs of r1 and r2.  If both point 1 and point 2 lie
    * on same side of second line segment, the line segments do
    * not intersect.  */

    if ( r1 != 0 &&
            r2 != 0 &&
            SAME_SIGNS( r1, r2 ))
    return ( DONT_INTERSECT );

    /* Line segments intersect: compute intersection point.  */

    denom = a1 * b2 - a2 * b1;
    if ( denom == 0 )
    return ( DONT_INTERSECT );
    offset = denom < 0 ? - denom / 2 : denom / 2;

    /* The denom/2 is to get rounding instead of truncating.  It
    * is added or subtracted to the numerator, depending upon the
    * sign of the numerator.  */

    num = b1 * c2 - b2 * c1;
    ix = ( num < 0 ? num - offset : num + offset ) / denom;

    num = a2 * c1 - a1 * c2;
    iy = ( num < 0 ? num - offset : num + offset ) / denom;

    return ( DO_INTERSECT );
}