pm_math.cpp

/***
*
*	Copyright (c) 1996-2002, Valve LLC. All rights reserved.
*	
*	This product contains software technology licensed from Id 
*	Software, Inc. ("Id Technology").  Id Technology (c) 1996 Id Software, Inc. 
*	All Rights Reserved.
*
*   Use, distribution, and modification of this source code and/or resulting
*   object code is restricted to non-commercial enhancements to products from
*   Valve LLC.  All other use, distribution, or modification is prohibited
*   without written permission from Valve LLC.
*
****/
// pm_math.c -- math primitives

#include "Platform.h"
#include "mathlib.h"
#include "const.h"

// up / down
#define PITCH 0
// left / right
#define YAW 1
// fall over
#define ROLL 2

#pragma warning(disable : 4244)

int nanmask = 255 << 23;

float anglemod(float a)
{
	a = (360.0 / 65536) * ((int)(a * (65536 / 360.0)) & 65535);
	return a;
}

void AngleVectors(const Vector& angles, Vector* forward, Vector* right, Vector* up)
{
	float angle;
	float sr, sp, sy, cr, cp, cy;

	angle = angles[YAW] * (M_PI * 2 / 360);
	sy = sin(angle);
	cy = cos(angle);
	angle = angles[PITCH] * (M_PI * 2 / 360);
	sp = sin(angle);
	cp = cos(angle);
	angle = angles[ROLL] * (M_PI * 2 / 360);
	sr = sin(angle);
	cr = cos(angle);

	if (forward)
	{
		forward->x = cp * cy;
		forward->y = cp * sy;
		forward->z = -sp;
	}
	if (right)
	{
		right->x = (-1 * sr * sp * cy + -1 * cr * -sy);
		right->y = (-1 * sr * sp * sy + -1 * cr * cy);
		right->z = -1 * sr * cp;
	}
	if (up)
	{
		up->x = (cr * sp * cy + -sr * -sy);
		up->y = (cr * sp * sy + -sr * cy);
		up->z = cr * cp;
	}
}

void AngleVectorsTranspose(const Vector& angles, Vector* forward, Vector* right, Vector* up)
{
	float angle;
	float sr, sp, sy, cr, cp, cy;

	angle = angles[YAW] * (M_PI * 2 / 360);
	sy = sin(angle);
	cy = cos(angle);
	angle = angles[PITCH] * (M_PI * 2 / 360);
	sp = sin(angle);
	cp = cos(angle);
	angle = angles[ROLL] * (M_PI * 2 / 360);
	sr = sin(angle);
	cr = cos(angle);

	if (forward)
	{
		forward->x = cp * cy;
		forward->y = (sr * sp * cy + cr * -sy);
		forward->z = (cr * sp * cy + -sr * -sy);
	}
	if (right)
	{
		right->x = cp * sy;
		right->y = (sr * sp * sy + cr * cy);
		right->z = (cr * sp * sy + -sr * cy);
	}
	if (up)
	{
		up->x = -sp;
		up->y = sr * cp;
		up->z = cr * cp;
	}
}

void AngleMatrix(const float* angles, float (*matrix)[4])
{
	float angle;
	float sr, sp, sy, cr, cp, cy;

	angle = angles[YAW] * (M_PI * 2 / 360);
	sy = sin(angle);
	cy = cos(angle);
	angle = angles[PITCH] * (M_PI * 2 / 360);
	sp = sin(angle);
	cp = cos(angle);
	angle = angles[ROLL] * (M_PI * 2 / 360);
	sr = sin(angle);
	cr = cos(angle);

	// matrix = (YAW * PITCH) * ROLL
	matrix[0][0] = cp * cy;
	matrix[1][0] = cp * sy;
	matrix[2][0] = -sp;
	matrix[0][1] = sr * sp * cy + cr * -sy;
	matrix[1][1] = sr * sp * sy + cr * cy;
	matrix[2][1] = sr * cp;
	matrix[0][2] = (cr * sp * cy + -sr * -sy);
	matrix[1][2] = (cr * sp * sy + -sr * cy);
	matrix[2][2] = cr * cp;
	matrix[0][3] = 0.0;
	matrix[1][3] = 0.0;
	matrix[2][3] = 0.0;
}

void AngleIMatrix(const Vector& angles, float matrix[3][4])
{
	float angle;
	float sr, sp, sy, cr, cp, cy;

	angle = angles[YAW] * (M_PI * 2 / 360);
	sy = sin(angle);
	cy = cos(angle);
	angle = angles[PITCH] * (M_PI * 2 / 360);
	sp = sin(angle);
	cp = cos(angle);
	angle = angles[ROLL] * (M_PI * 2 / 360);
	sr = sin(angle);
	cr = cos(angle);

	// matrix = (YAW * PITCH) * ROLL
	matrix[0][0] = cp * cy;
	matrix[0][1] = cp * sy;
	matrix[0][2] = -sp;
	matrix[1][0] = sr * sp * cy + cr * -sy;
	matrix[1][1] = sr * sp * sy + cr * cy;
	matrix[1][2] = sr * cp;
	matrix[2][0] = (cr * sp * cy + -sr * -sy);
	matrix[2][1] = (cr * sp * sy + -sr * cy);
	matrix[2][2] = cr * cp;
	matrix[0][3] = 0.0;
	matrix[1][3] = 0.0;
	matrix[2][3] = 0.0;
}

void NormalizeAngles(float* angles)
{
	int i;
	// Normalize angles
	for (i = 0; i < 3; i++)
	{
		if (angles[i] > 180.0)
		{
			angles[i] -= 360.0;
		}
		else if (angles[i] < -180.0)
		{
			angles[i] += 360.0;
		}
	}
}

/*
===================
InterpolateAngles

Interpolate Euler angles.
FIXME:  Use Quaternions to avoid discontinuities
Frac is 0.0 to 1.0 ( i.e., should probably be clamped, but doesn't have to be )
===================
*/
void InterpolateAngles(float* start, float* end, float* output, float frac)
{
	int i;
	float ang1, ang2;
	float d;

	NormalizeAngles(start);
	NormalizeAngles(end);

	for (i = 0; i < 3; i++)
	{
		ang1 = start[i];
		ang2 = end[i];

		d = ang2 - ang1;
		if (d > 180)
		{
			d -= 360;
		}
		else if (d < -180)
		{
			d += 360;
		}

		output[i] = ang1 + d * frac;
	}

	NormalizeAngles(output);
}


/*
===================
AngleBetweenVectors

===================
*/
float AngleBetweenVectors(const Vector& v1, const Vector& v2)
{
	float angle;
	float l1 = Length(v1);
	float l2 = Length(v2);

	if (0 == l1 || 0 == l2)
		return 0.0f;

	angle = acos(DotProduct(v1, v2)) / (l1 * l2);
	angle = (angle * 180.0f) / M_PI;

	return angle;
}

void VectorTransform(const float* in1, float in2[3][4], float* out)
{
	out[0] = DotProduct(*reinterpret_cast<const Vector*>(in1), *reinterpret_cast<const Vector*>(in2[0])) + in2[0][3];
	out[1] = DotProduct(*reinterpret_cast<const Vector*>(in1), *reinterpret_cast<const Vector*>(in2[1])) + in2[1][3];
	out[2] = DotProduct(*reinterpret_cast<const Vector*>(in1), *reinterpret_cast<const Vector*>(in2[2])) + in2[2][3];
}

bool VectorCompare(const float* v1, const float* v2)
{
	int i;

	for (i = 0; i < 3; i++)
		if (v1[i] != v2[i])
			return false;

	return true;
}

void VectorMA(const float* veca, float scale, const float* vecb, float* vecc)
{
	vecc[0] = veca[0] + scale * vecb[0];
	vecc[1] = veca[1] + scale * vecb[1];
	vecc[2] = veca[2] + scale * vecb[2];
}

void CrossProduct(const float* v1, const float* v2, float* cross)
{
	cross[0] = v1[1] * v2[2] - v1[2] * v2[1];
	cross[1] = v1[2] * v2[0] - v1[0] * v2[2];
	cross[2] = v1[0] * v2[1] - v1[1] * v2[0];
}

float Length(const float* v)
{
	int i;
	float length = 0.0f;

	for (i = 0; i < 3; i++)
		length += v[i] * v[i];
	length = sqrt(length); // FIXME

	return length;
}

float Distance(const float* v1, const float* v2)
{
	Vector d;
	VectorSubtract(v2, v1, d);
	return Length(d);
}

float VectorNormalize(float* v)
{
	float length, ilength;

	length = v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
	length = sqrt(length); // FIXME

	if (0 != length)
	{
		ilength = 1 / length;
		v[0] *= ilength;
		v[1] *= ilength;
		v[2] *= ilength;
	}

	return length;
}

void VectorInverse(float* v)
{
	v[0] = -v[0];
	v[1] = -v[1];
	v[2] = -v[2];
}

void VectorScale(const float* in, float scale, float* out)
{
	out[0] = in[0] * scale;
	out[1] = in[1] * scale;
	out[2] = in[2] * scale;
}

int Q_log2(int val)
{
	int answer = 0;
	while ((val >>= 1) != 0)
		answer++;
	return answer;
}

void VectorMatrix(const Vector& forward, Vector& right, Vector& up)
{
	Vector tmp;

	if (forward[0] == 0 && forward[1] == 0)
	{
		right[0] = 1;
		right[1] = 0;
		right[2] = 0;
		up[0] = -forward[2];
		up[1] = 0;
		up[2] = 0;
		return;
	}

	tmp[0] = 0;
	tmp[1] = 0;
	tmp[2] = 1.0;
	CrossProduct(forward, tmp, right);
	VectorNormalize(right);
	CrossProduct(right, forward, up);
	VectorNormalize(up);
}

void VectorAngles(const float* forward, float* angles)
{
	double tmp, yaw, pitch;

	if (forward[1] == 0 && forward[0] == 0)
	{
		yaw = 0;
		if (forward[2] > 0)
			pitch = 90;
		else
			pitch = 270;
	}
	else
	{
		yaw = (atan2(forward[1], forward[0]) * 180 / M_PI);
		if (yaw < 0)
			yaw += 360;

		tmp = sqrt(forward[0] * forward[0] + forward[1] * forward[1]);
		pitch = (atan2(forward[2], tmp) * 180 / M_PI);
		if (pitch < 0)
			pitch += 360;
	}

	angles[0] = pitch;
	angles[1] = yaw;
	angles[2] = 0;
}

/*
================
ConcatTransforms

================
*/
void ConcatTransforms(float in1[3][4], float in2[3][4], float out[3][4])
{
	out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
				in1[0][2] * in2[2][0];
	out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
				in1[0][2] * in2[2][1];
	out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
				in1[0][2] * in2[2][2];
	out[0][3] = in1[0][0] * in2[0][3] + in1[0][1] * in2[1][3] +
				in1[0][2] * in2[2][3] + in1[0][3];
	out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
				in1[1][2] * in2[2][0];
	out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
				in1[1][2] * in2[2][1];
	out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
				in1[1][2] * in2[2][2];
	out[1][3] = in1[1][0] * in2[0][3] + in1[1][1] * in2[1][3] +
				in1[1][2] * in2[2][3] + in1[1][3];
	out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
				in1[2][2] * in2[2][0];
	out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
				in1[2][2] * in2[2][1];
	out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
				in1[2][2] * in2[2][2];
	out[2][3] = in1[2][0] * in2[0][3] + in1[2][1] * in2[1][3] +
				in1[2][2] * in2[2][3] + in1[2][3];
}