veclib4d.c

[Game.Programming].Academic - Graphics Gems (6 books source code)

 * ie. Identity, Rotation (6 kinds), Translation and Scaling.
 */

/* V4MatIdentity()
 *
 * Initialises to identity matrix.
 */

Matrix5 *
V4MatIdentity(mat)
Matrix5	*mat;
{
	int	i, j;

	for (i = 0; i < 5; i += 1)
	for (j = 0; j < 5; j += 1)
		mat->element[i][j] = i == j ? 1.0 : 0.0;
}

/* V4MatRotationXY() etc.
 *
 * Initialises a matrix to a rotation by theta about the indicated hyperplane.
 */

Matrix5 *
V4MatRotationXY(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	s, c;

	s = sin(theta);
	c = cos(theta);

	V4MatIdentity(mat);
	mat->element[0][0] = c;
	mat->element[0][1] = s;
	mat->element[1][0] = -s;
	mat->element[1][1] = c;

	return mat;
}

Matrix5 *
V4MatRotationXW(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	s, c;

	s = sin(theta);
	c = cos(theta);

	V4MatIdentity(mat);
	mat->element[0][0] = c;
	mat->element[0][3] = s;
	mat->element[3][0] = -s;
	mat->element[3][3] = c;

	return mat;
}

Matrix5 *
V4MatRotationYZ(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	s, c;

	s = sin(theta);
	c = cos(theta);

	V4MatIdentity(mat);
	mat->element[1][1] = c;
	mat->element[1][2] = s;
	mat->element[2][1] = -s;
	mat->element[2][2] = c;

	return mat;
}

Matrix5 *
V4MatRotationYW(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	s, c;

	s = sin(theta);
	c = cos(theta);

	V4MatIdentity(mat);
	mat->element[1][1] = c;
	mat->element[1][3] = -s;
	mat->element[3][1] = s;
	mat->element[3][3] = c;

	return mat;
}

Matrix5 *
V4MatRotationZX(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	s, c;

	s = sin(theta);
	c = cos(theta);

	V4MatIdentity(mat);
	mat->element[0][0] = c;
	mat->element[0][2] = -s;
	mat->element[2][0] = s;
	mat->element[2][2] = c;

	return mat;
}

Matrix5 *
V4MatRotationZW(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	s, c;

	s = sin(theta);
	c = cos(theta);

	V4MatIdentity(mat);
	mat->element[2][2] = c;
	mat->element[2][3] = -s;
	mat->element[3][2] = s;
	mat->element[3][3] = c;

	return mat;
}

/* V4MatTranslation()
 *
 * Initialise a matrix to the translation v
 */

Matrix5 *
V4MatTranslation(mat, v)
Matrix5	*mat;
Vector4	*v;
{
	V4MatIdentity(mat);
	mat->element[4][0] = v->x;
	mat->element[4][1] = v->y;
	mat->element[4][2] = v->z;
	mat->element[4][3] = v->w;

	return mat;
}

/* V4MatScaling()
 *
 * Initialise a matrix to the scaling v
 */

Matrix5 *
V4MatScaling(mat, v)
Matrix5	*mat;
Vector4	*v;
{
	V4MatIdentity(mat);
	mat->element[0][0] = v->x;
	mat->element[1][1] = v->y;
	mat->element[2][2] = v->z;
	mat->element[3][3] = v->w;

	return mat;
}

/* MATRIX OPERATIONS
 *
 * The following functions are provided for a fast compact method
 * to create compound transformations.  Matrix multiplication has
 * been folded into the functions thus eliminating the need for
 * many redundant calculations.  For sparse matrices containing
 * mainly just ones and zeros this represents a considerable saving.
 *
 * Each function takes the form F(M, args) and has the effect
 * M := M o F1(args) where F1 is the transformation corresponding
 * to F.
 */

Matrix5	*
V4MatRotateXY(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	a, b, f, g, k, l, p, q, u, v;
	double	st, ct;

	st = sin(theta);
	ct = cos(theta);

	a = mat->element[0][0]; b = mat->element[0][1];
	f = mat->element[1][0]; g = mat->element[1][1];
	k = mat->element[2][0]; l = mat->element[2][1];
	p = mat->element[3][0]; q = mat->element[3][1];
	u = mat->element[4][0]; v = mat->element[4][1];

	mat->element[0][0] = a * ct - b * st;
	mat->element[0][1] = a * st + b * ct;
	mat->element[1][0] = f * ct - g * st;
	mat->element[1][1] = f * st + g * ct;
	mat->element[2][0] = k * ct - l * st;
	mat->element[2][1] = k * st + l * ct;
	mat->element[3][0] = p * ct - q * st;
	mat->element[3][1] = p * st + q * ct;
	mat->element[4][0] = u * ct - v * st;
	mat->element[4][1] = u * st + v * ct;

	return mat;
}

Matrix5	*
V4MatRotateXW(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	a, d, f, i, k, n, p, s, u, x;
	double	st, ct;

	st = sin(theta);
	ct = cos(theta);

	a = mat->element[0][0]; d = mat->element[0][3];
	f = mat->element[1][0]; i = mat->element[1][3];
	k = mat->element[2][0]; n = mat->element[2][3];
	p = mat->element[3][0]; s = mat->element[3][3];
	u = mat->element[4][0]; x = mat->element[4][3];

	mat->element[0][0] = a * ct - d * st;
	mat->element[0][3] = a * st + d * ct;
	mat->element[1][0] = f * ct - i * st;
	mat->element[1][3] = f * st + i * ct;
	mat->element[2][0] = k * ct - n * st;
	mat->element[2][3] = k * st + n * ct;
	mat->element[3][0] = p * ct - s * st;
	mat->element[3][3] = p * st + s * ct;
	mat->element[4][0] = u * ct - x * st;
	mat->element[4][3] = u * st + x * ct;

	return mat;
}

Matrix5	*
V4MatRotateYZ(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	b, c, g, h, l, m, q, r, v, w;
	double st, ct;

	st = sin(theta);
	ct = cos(theta);

	b = mat->element[0][1]; c = mat->element[0][2];
	g = mat->element[1][1]; h = mat->element[1][2];
	l = mat->element[2][1]; m = mat->element[2][2];
	q = mat->element[3][1]; r = mat->element[3][2];
	v = mat->element[4][1]; w = mat->element[4][2];

	mat->element[0][1] = b * ct - c * st;
	mat->element[0][2] = b * st + c * ct;
	mat->element[1][1] = g * ct - h * st;
	mat->element[1][2] = g * st + h * ct;
	mat->element[2][1] = l * ct - m * st;
	mat->element[2][2] = l * st + m * ct;
	mat->element[3][1] = q * ct - r * st;
	mat->element[3][2] = q * st + r * ct;
	mat->element[4][1] = v * ct - w * st;
	mat->element[4][2] = v * st + w * ct;

	return mat;
}

Matrix5	*
V4MatRotateYW(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	b, d, g, i, l, n, q, s, v, x;
	double	st, ct;

	st = sin(theta);
	ct = cos(theta);

	b = mat->element[0][1]; d = mat->element[0][3];
	g = mat->element[1][1]; i = mat->element[1][3];
	l = mat->element[2][1]; n = mat->element[2][3];
	q = mat->element[3][1]; s = mat->element[3][3];
	v = mat->element[4][1]; x = mat->element[4][3];

	mat->element[0][1] =   b * ct + d * st;
	mat->element[0][3] = - b * st + d * ct;
	mat->element[1][1] =   g * ct + i * st;
	mat->element[1][3] = - g * st + i * ct;
	mat->element[2][1] =   l * ct + n * st;
	mat->element[2][3] = - l * st + n * ct;
	mat->element[3][1] =   q * ct + s * st;
	mat->element[3][3] = - q * st + s * ct;
	mat->element[4][1] =   v * ct + x * st;
	mat->element[4][3] = - v * st + x * ct;

	return mat;
}

Matrix5	*
V4MatRotateZX(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	a, c, f, h, k, m, p, r, u, w;
	double	st, ct;

	st = sin(theta);
	ct = cos(theta);

	a = mat->element[0][0]; c = mat->element[0][2];
	f = mat->element[1][0]; h = mat->element[1][2];
	k = mat->element[2][0]; m = mat->element[2][2];
	p = mat->element[3][0]; r = mat->element[3][2];
	u = mat->element[4][0]; w = mat->element[4][2];

	mat->element[0][0] =   a * ct + c * st;
	mat->element[0][2] = - a * st + c * ct;
	mat->element[1][0] =   f * ct + h * st;
	mat->element[1][2] = - f * st + h * ct;
	mat->element[2][0] =   k * ct + m * st;
	mat->element[2][2] = - k * st + m * ct;
	mat->element[3][0] =   p * ct + r * st;
	mat->element[3][2] = - p * st + r * ct;
	mat->element[4][0] =   u * ct + w * st;
	mat->element[4][2] = - u * st + w * ct;

	return mat;
}


Matrix5	*
V4MatRotateZW(mat, theta)
Matrix5	*mat;
double	theta;
{
	double	c, d, h, i, m, n, r, s, w, x;
	double	st, ct;

	st = sin(theta);
	ct = cos(theta);

	c = mat->element[0][2]; d = mat->element[0][3];
	h = mat->element[1][2]; i = mat->element[1][3];
	m = mat->element[2][2]; n = mat->element[2][3];
	r = mat->element[3][2]; s = mat->element[3][3];
	w = mat->element[4][2]; x = mat->element[4][3];

	mat->element[0][2] =   c * ct + d * st;
	mat->element[0][3] = - c * st + d * ct;
	mat->element[1][2] =   h * ct + i * st;
	mat->element[1][3] = - h * st + i * ct;
	mat->element[2][2] =   m * ct + n * st;
	mat->element[2][3] = - m * st + n * ct;
	mat->element[3][2] =   r * ct + s * st;
	mat->element[3][3] = - r * st + s * ct;
	mat->element[4][2] =   w * ct + x * st;
	mat->element[4][3] = - w * st + x * ct;

	return mat;
}

Matrix5	*
V4MatTranslate(mat, v)
Matrix5	*mat;
Vector4	*v;
{
	double	e, j, o, t, y;

	e = mat->element[0][4];
	j = mat->element[1][4];
	o = mat->element[2][4];
	t = mat->element[3][4];
	y = mat->element[4][4];

	if (e != 0.0)
	{
		mat->element[0][0] += e * v->x;
		mat->element[0][1] += e * v->y;
		mat->element[0][2] += e * v->z;
		mat->element[0][3] += e * v->w;
	}
	if (j != 0.0)
	{
		mat->element[1][0] += j * v->x;
		mat->element[1][1] += j * v->y;
		mat->element[1][2] += j * v->z;
		mat->element[1][3] += j * v->w;
	}
	if (o != 0.0)
	{
		mat->element[2][0] += o * v->x;
		mat->element[2][1] += o * v->y;
		mat->element[2][2] += o * v->z;
		mat->element[2][3] += o * v->w;
	}
	if (t != 0.0)
	{
		mat->element[3][0] += t * v->x;
		mat->element[3][1] += t * v->y;
		mat->element[3][2] += t * v->z;
		mat->element[3][3] += t * v->w;
	}
	if (y != 0.0)
	{
		mat->element[4][0] += y * v->x;
		mat->element[4][1] += y * v->y;
		mat->element[4][2] += y * v->z;
		mat->element[4][3] += y * v->w;
	}

	return mat;
}

Matrix5 *
V4MatScale(mat, v)
Matrix5	*mat;
Vector4	*v;
{
	if (v->x != 1.0)
	{
		mat->element[0][0] *= v->x;
		mat->element[1][0] *= v->x;
		mat->element[2][0] *= v->x;
		mat->element[3][0] *= v->x;
		mat->element[4][0] *= v->x;
	}
	if (v->y != 1.0)
	{
		mat->element[0][1] *= v->y;
		mat->element[1][1] *= v->y;
		mat->element[2][1] *= v->y;
		mat->element[3][1] *= v->y;
		mat->element[4][1] *= v->y;
	}
	if (v->z != 1.0)
	{
		mat->element[0][2] *= v->z;
		mat->element[1][2] *= v->z;
		mat->element[2][2] *= v->z;
		mat->element[3][2] *= v->z;
		mat->element[4][2] *= v->z;
	}
	if (v->w != 1.0)
	{
		mat->element[0][3] *= v->w;
		mat->element[1][3] *= v->w;
		mat->element[2][3] *= v->w;
		mat->element[3][3] *= v->w;
		mat->element[4][3] *= v->w;
	}

	return mat;
}

/* Postscript
 *
 * The elements of the 5x5 matrix are labelled in the above functions
 * as follows:
 *
 * a = mat->element[0][0];
 * b = mat->element[0][1];
 * c = mat->element[0][2];
 * d = mat->element[0][3];
 * e = mat->element[0][4];
 * f = mat->element[1][0];
 * g = mat->element[1][1];
 * h = mat->element[1][2];
 * i = mat->element[1][3];
 * j = mat->element[1][4];
 * k = mat->element[2][0];
 * l = mat->element[2][1];
 * m = mat->element[2][2];
 * n = mat->element[2][3];
 * o = mat->element[2][4];
 * p = mat->element[3][0];
 * q = mat->element[3][1];
 * r = mat->element[3][2];
 * s = mat->element[3][3];
 * t = mat->element[3][4];
 * u = mat->element[4][0];
 * v = mat->element[4][1];
 * w = mat->element[4][2];
 * x = mat->element[4][3];
 * y = mat->element[4][4];
 *
 * ie.
 * [ a b c d e ]
 * [ f g h i j ]
 * [ k l m n o ]
 * [ p q r s t ]
 * [ u v w x y ]
 *
 */