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sm64pc/src/engine/math_util.c

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#include <ultra64.h>
#include "sm64.h"
#include "engine/graph_node.h"
#include "math_util.h"
#include "surface_collision.h"
#include "trig_tables.inc.c"
// Variables for a spline curve animation (used for the flight path in the grand star cutscene)
Vec4s *gSplineKeyframe;
float gSplineKeyframeFraction;
int gSplineState;
// These functions have bogus return values.
// Disable the compiler warning.
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wreturn-local-addr"
/// Copy vector 'src' to 'dest'
void *vec3f_copy(Vec3f dest, Vec3f src) {
dest[0] = src[0];
dest[1] = src[1];
dest[2] = src[2];
return &dest; //! warning: function returns address of local variable
}
/// Set vector 'dest' to (x, y, z)
void *vec3f_set(Vec3f dest, f32 x, f32 y, f32 z) {
dest[0] = x;
dest[1] = y;
dest[2] = z;
return &dest; //! warning: function returns address of local variable
}
/// Add vector 'a' to 'dest'
void *vec3f_add(Vec3f dest, Vec3f a) {
dest[0] += a[0];
dest[1] += a[1];
dest[2] += a[2];
return &dest; //! warning: function returns address of local variable
}
/// Make 'dest' the sum of vectors a and b.
void *vec3f_sum(Vec3f dest, Vec3f a, Vec3f b) {
dest[0] = a[0] + b[0];
dest[1] = a[1] + b[1];
dest[2] = a[2] + b[2];
return &dest; //! warning: function returns address of local variable
}
/// Multiply vector 'dest' by a
void *vec3f_mul(Vec3f dest, f32 a)
{
dest[0] *= a;
dest[1] *= a;
dest[2] *= a;
return &dest; //! warning: function returns address of local variable
}
/// Copy vector src to dest
void *vec3s_copy(Vec3s dest, Vec3s src) {
dest[0] = src[0];
dest[1] = src[1];
dest[2] = src[2];
return &dest; //! warning: function returns address of local variable
}
/// Set vector 'dest' to (x, y, z)
void *vec3s_set(Vec3s dest, s16 x, s16 y, s16 z) {
dest[0] = x;
dest[1] = y;
dest[2] = z;
return &dest; //! warning: function returns address of local variable
}
/// Add vector a to 'dest'
void *vec3s_add(Vec3s dest, Vec3s a) {
dest[0] += a[0];
dest[1] += a[1];
dest[2] += a[2];
return &dest; //! warning: function returns address of local variable
}
/// Make 'dest' the sum of vectors a and b.
void *vec3s_sum(Vec3s dest, Vec3s a, Vec3s b) {
dest[0] = a[0] + b[0];
dest[1] = a[1] + b[1];
dest[2] = a[2] + b[2];
return &dest; //! warning: function returns address of local variable
}
/// Make 'dest' the difference of vectors a and b.
void *vec3f_dif(Vec3f dest, Vec3f a, Vec3f b) {
dest[0] = a[0] - b[0];
dest[1] = a[1] - b[1];
dest[2] = a[2] - b[2];
return &dest; //! warning: function returns address of local variable
}
/// Convert short vector a to float vector 'dest'
void *vec3s_to_vec3f(Vec3f dest, Vec3s a) {
dest[0] = a[0];
dest[1] = a[1];
dest[2] = a[2];
return &dest; //! warning: function returns address of local variable
}
/**
* Convert float vector a to a short vector 'dest' by rounding the components
* to the nearest integer.
*/
void *vec3f_to_vec3s(Vec3s dest, Vec3f a) {
// add/subtract 0.5 in order to round to the nearest s32 instead of truncating
dest[0] = a[0] + ((a[0] > 0) ? 0.5f : -0.5f);
dest[1] = a[1] + ((a[1] > 0) ? 0.5f : -0.5f);
dest[2] = a[2] + ((a[2] > 0) ? 0.5f : -0.5f);
return &dest; //! warning: function returns address of local variable
}
/**
* Set 'dest' the normal vector of a triangle with vertices a, b and c.
* It is similar to vec3f_cross, but it calculates the vectors (c-b) and (b-a)
* at the same time.
*/
void *find_vector_perpendicular_to_plane(Vec3f dest, Vec3f a, Vec3f b, Vec3f c) {
dest[0] = (b[1] - a[1]) * (c[2] - b[2]) - (c[1] - b[1]) * (b[2] - a[2]);
dest[1] = (b[2] - a[2]) * (c[0] - b[0]) - (c[2] - b[2]) * (b[0] - a[0]);
dest[2] = (b[0] - a[0]) * (c[1] - b[1]) - (c[0] - b[0]) * (b[1] - a[1]);
return &dest; //! warning: function returns address of local variable
}
/// Make vector 'dest' the cross product of vectors a and b.
void *vec3f_cross(Vec3f dest, Vec3f a, Vec3f b) {
dest[0] = a[1] * b[2] - b[1] * a[2];
dest[1] = a[2] * b[0] - b[2] * a[0];
dest[2] = a[0] * b[1] - b[0] * a[1];
return &dest; //! warning: function returns address of local variable
}
/// Scale vector 'dest' so it has length 1
void *vec3f_normalize(Vec3f dest) {
//! Possible division by zero
f32 invsqrt = 1.0f / sqrtf(dest[0] * dest[0] + dest[1] * dest[1] + dest[2] * dest[2]);
dest[0] *= invsqrt;
dest[1] *= invsqrt;
dest[2] *= invsqrt;
return &dest; //! warning: function returns address of local variable
}
/// Get length of vector 'a'
f32 vec3f_length(Vec3f a)
{
return sqrtf(a[0] * a[0] + a[1] * a[1] + a[2] * a[2]);
}
/// Get dot product of vectors 'a' and 'b'
f32 vec3f_dot(Vec3f a, Vec3f b)
{
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}
#pragma GCC diagnostic pop
/// Copy matrix 'src' to 'dest'
void mtxf_copy(Mat4 dest, Mat4 src) {
register s32 i;
register u32 *d = (u32 *) dest;
register u32 *s = (u32 *) src;
for (i = 0; i < 16; i++) {
*d++ = *s++;
}
}
/**
* Set mtx to the identity matrix
*/
void mtxf_identity(Mat4 mtx) {
register s32 i;
register f32 *dest;
// Note: These loops need to be on one line to match on PAL
// initialize everything except the first and last cells to 0
for (dest = (f32 *) mtx + 1, i = 0; i < 14; dest++, i++) *dest = 0;
// initialize the diagonal cells to 1
for (dest = (f32 *) mtx, i = 0; i < 4; dest += 5, i++) *dest = 1;
}
/**
* Set dest to a translation matrix of vector b
*/
void mtxf_translate(Mat4 dest, Vec3f b) {
mtxf_identity(dest);
dest[3][0] = b[0];
dest[3][1] = b[1];
dest[3][2] = b[2];
}
/**
* Set mtx to a look-at matrix for the camera. The resulting transformation
* transforms the world as if there exists a camera at position 'from' pointed
* at the position 'to'. The up-vector is assumed to be (0, 1, 0), but the 'roll'
* angle allows a bank rotation of the camera.
*/
void mtxf_lookat(Mat4 mtx, Vec3f from, Vec3f to, s16 roll) {
register f32 invLength;
f32 dx;
f32 dz;
f32 xColY;
f32 yColY;
f32 zColY;
f32 xColZ;
f32 yColZ;
f32 zColZ;
f32 xColX;
f32 yColX;
f32 zColX;
dx = to[0] - from[0];
dz = to[2] - from[2];
invLength = -1.0 / sqrtf(dx * dx + dz * dz);
dx *= invLength;
dz *= invLength;
yColY = coss(roll);
xColY = sins(roll) * dz;
zColY = -sins(roll) * dx;
xColZ = to[0] - from[0];
yColZ = to[1] - from[1];
zColZ = to[2] - from[2];
invLength = -1.0 / sqrtf(xColZ * xColZ + yColZ * yColZ + zColZ * zColZ);
xColZ *= invLength;
yColZ *= invLength;
zColZ *= invLength;
xColX = yColY * zColZ - zColY * yColZ;
yColX = zColY * xColZ - xColY * zColZ;
zColX = xColY * yColZ - yColY * xColZ;
invLength = 1.0 / sqrtf(xColX * xColX + yColX * yColX + zColX * zColX);
xColX *= invLength;
yColX *= invLength;
zColX *= invLength;
xColY = yColZ * zColX - zColZ * yColX;
yColY = zColZ * xColX - xColZ * zColX;
zColY = xColZ * yColX - yColZ * xColX;
invLength = 1.0 / sqrtf(xColY * xColY + yColY * yColY + zColY * zColY);
xColY *= invLength;
yColY *= invLength;
zColY *= invLength;
mtx[0][0] = xColX;
mtx[1][0] = yColX;
mtx[2][0] = zColX;
mtx[3][0] = -(from[0] * xColX + from[1] * yColX + from[2] * zColX);
mtx[0][1] = xColY;
mtx[1][1] = yColY;
mtx[2][1] = zColY;
mtx[3][1] = -(from[0] * xColY + from[1] * yColY + from[2] * zColY);
mtx[0][2] = xColZ;
mtx[1][2] = yColZ;
mtx[2][2] = zColZ;
mtx[3][2] = -(from[0] * xColZ + from[1] * yColZ + from[2] * zColZ);
mtx[0][3] = 0;
mtx[1][3] = 0;
mtx[2][3] = 0;
mtx[3][3] = 1;
}
/**
* Build a matrix that rotates around the z axis, then the x axis, then the y
* axis, and then translates.
*/
void mtxf_rotate_zxy_and_translate(Mat4 dest, Vec3f translate, Vec3s rotate) {
register f32 sx = sins(rotate[0]);
register f32 cx = coss(rotate[0]);
register f32 sy = sins(rotate[1]);
register f32 cy = coss(rotate[1]);
register f32 sz = sins(rotate[2]);
register f32 cz = coss(rotate[2]);
dest[0][0] = cy * cz + sx * sy * sz;
dest[1][0] = -cy * sz + sx * sy * cz;
dest[2][0] = cx * sy;
dest[3][0] = translate[0];
dest[0][1] = cx * sz;
dest[1][1] = cx * cz;
dest[2][1] = -sx;
dest[3][1] = translate[1];
dest[0][2] = -sy * cz + sx * cy * sz;
dest[1][2] = sy * sz + sx * cy * cz;
dest[2][2] = cx * cy;
dest[3][2] = translate[2];
dest[0][3] = dest[1][3] = dest[2][3] = 0.0f;
dest[3][3] = 1.0f;
}
/**
* Build a matrix that rotates around the x axis, then the y axis, then the z
* axis, and then translates.
*/
void mtxf_rotate_xyz_and_translate(Mat4 dest, Vec3f b, Vec3s c) {
register f32 sx = sins(c[0]);
register f32 cx = coss(c[0]);
register f32 sy = sins(c[1]);
register f32 cy = coss(c[1]);
register f32 sz = sins(c[2]);
register f32 cz = coss(c[2]);
dest[0][0] = cy * cz;
dest[0][1] = cy * sz;
dest[0][2] = -sy;
dest[0][3] = 0;
dest[1][0] = sx * sy * cz - cx * sz;
dest[1][1] = sx * sy * sz + cx * cz;
dest[1][2] = sx * cy;
dest[1][3] = 0;
dest[2][0] = cx * sy * cz + sx * sz;
dest[2][1] = cx * sy * sz - sx * cz;
dest[2][2] = cx * cy;
dest[2][3] = 0;
dest[3][0] = b[0];
dest[3][1] = b[1];
dest[3][2] = b[2];
dest[3][3] = 1;
}
/**
* Set 'dest' to a transformation matrix that turns an object to face the camera.
* 'mtx' is the look-at matrix from the camera
* 'position' is the position of the object in the world
* 'angle' rotates the object while still facing the camera.
*/
void mtxf_billboard(Mat4 dest, Mat4 mtx, Vec3f position, s16 angle) {
dest[0][0] = coss(angle);
dest[0][1] = sins(angle);
dest[0][2] = 0;
dest[0][3] = 0;
dest[1][0] = -dest[0][1];
dest[1][1] = dest[0][0];
dest[1][2] = 0;
dest[1][3] = 0;
dest[2][0] = 0;
dest[2][1] = 0;
dest[2][2] = 1;
dest[2][3] = 0;
dest[3][0] =
mtx[0][0] * position[0] + mtx[1][0] * position[1] + mtx[2][0] * position[2] + mtx[3][0];
dest[3][1] =
mtx[0][1] * position[0] + mtx[1][1] * position[1] + mtx[2][1] * position[2] + mtx[3][1];
dest[3][2] =
mtx[0][2] * position[0] + mtx[1][2] * position[1] + mtx[2][2] * position[2] + mtx[3][2];
dest[3][3] = 1;
}
/**
* Set 'dest' to a transformation matrix that aligns an object with the terrain
* based on the normal. Used for enemies.
* 'upDir' is the terrain normal
* 'yaw' is the angle which it should face
* 'pos' is the object's position in the world
*/
void mtxf_align_terrain_normal(Mat4 dest, Vec3f upDir, Vec3f pos, s16 yaw) {
Vec3f lateralDir;
Vec3f leftDir;
Vec3f forwardDir;
vec3f_set(lateralDir, sins(yaw), 0, coss(yaw));
vec3f_normalize(upDir);
vec3f_cross(leftDir, upDir, lateralDir);
vec3f_normalize(leftDir);
vec3f_cross(forwardDir, leftDir, upDir);
vec3f_normalize(forwardDir);
dest[0][0] = leftDir[0];
dest[0][1] = leftDir[1];
dest[0][2] = leftDir[2];
dest[3][0] = pos[0];
dest[1][0] = upDir[0];
dest[1][1] = upDir[1];
dest[1][2] = upDir[2];
dest[3][1] = pos[1];
dest[2][0] = forwardDir[0];
dest[2][1] = forwardDir[1];
dest[2][2] = forwardDir[2];
dest[3][2] = pos[2];
dest[0][3] = 0.0f;
dest[1][3] = 0.0f;
dest[2][3] = 0.0f;
dest[3][3] = 1.0f;
}
/**
* Set 'mtx' to a transformation matrix that aligns an object with the terrain
* based on 3 height samples in an equilateral triangle around the object.
* Used for Mario when crawling or sliding.
* 'yaw' is the angle which it should face
* 'pos' is the object's position in the world
* 'radius' is the distance from each triangle vertex to the center
*/
void mtxf_align_terrain_triangle(Mat4 mtx, Vec3f pos, s16 yaw, f32 radius) {
struct Surface *sp74;
Vec3f point0;
Vec3f point1;
Vec3f point2;
Vec3f forward;
Vec3f xColumn;
Vec3f yColumn;
Vec3f zColumn;
f32 avgY;
f32 minY = -radius * 3;
point0[0] = pos[0] + radius * sins(yaw + 0x2AAA);
point0[2] = pos[2] + radius * coss(yaw + 0x2AAA);
point1[0] = pos[0] + radius * sins(yaw + 0x8000);
point1[2] = pos[2] + radius * coss(yaw + 0x8000);
point2[0] = pos[0] + radius * sins(yaw + 0xD555);
point2[2] = pos[2] + radius * coss(yaw + 0xD555);
point0[1] = find_floor(point0[0], pos[1] + 150, point0[2], &sp74);
point1[1] = find_floor(point1[0], pos[1] + 150, point1[2], &sp74);
point2[1] = find_floor(point2[0], pos[1] + 150, point2[2], &sp74);
if (point0[1] - pos[1] < minY) {
point0[1] = pos[1];
}
if (point1[1] - pos[1] < minY) {
point1[1] = pos[1];
}
if (point2[1] - pos[1] < minY) {
point2[1] = pos[1];
}
avgY = (point0[1] + point1[1] + point2[1]) / 3;
vec3f_set(forward, sins(yaw), 0, coss(yaw));
find_vector_perpendicular_to_plane(yColumn, point0, point1, point2);
vec3f_normalize(yColumn);
vec3f_cross(xColumn, yColumn, forward);
vec3f_normalize(xColumn);
vec3f_cross(zColumn, xColumn, yColumn);
vec3f_normalize(zColumn);
mtx[0][0] = xColumn[0];
mtx[0][1] = xColumn[1];
mtx[0][2] = xColumn[2];
mtx[3][0] = pos[0];
mtx[1][0] = yColumn[0];
mtx[1][1] = yColumn[1];
mtx[1][2] = yColumn[2];
mtx[3][1] = (avgY < pos[1]) ? pos[1] : avgY;
mtx[2][0] = zColumn[0];
mtx[2][1] = zColumn[1];
mtx[2][2] = zColumn[2];
mtx[3][2] = pos[2];
mtx[0][3] = 0;
mtx[1][3] = 0;
mtx[2][3] = 0;
mtx[3][3] = 1;
}
/**
* Sets matrix 'dest' to the matrix product b * a assuming they are both
* transformation matrices with a w-component of 1. Since the bottom row
* is assumed to equal [0, 0, 0, 1], it saves some multiplications and
* addition.
* The resulting matrix represents first applying transformation b and
* then a.
*/
void mtxf_mul(Mat4 dest, Mat4 a, Mat4 b) {
Mat4 temp;
register f32 entry0;
register f32 entry1;
register f32 entry2;
// column 0
entry0 = a[0][0];
entry1 = a[0][1];
entry2 = a[0][2];
temp[0][0] = entry0 * b[0][0] + entry1 * b[1][0] + entry2 * b[2][0];
temp[0][1] = entry0 * b[0][1] + entry1 * b[1][1] + entry2 * b[2][1];
temp[0][2] = entry0 * b[0][2] + entry1 * b[1][2] + entry2 * b[2][2];
// column 1
entry0 = a[1][0];
entry1 = a[1][1];
entry2 = a[1][2];
temp[1][0] = entry0 * b[0][0] + entry1 * b[1][0] + entry2 * b[2][0];
temp[1][1] = entry0 * b[0][1] + entry1 * b[1][1] + entry2 * b[2][1];
temp[1][2] = entry0 * b[0][2] + entry1 * b[1][2] + entry2 * b[2][2];
// column 2
entry0 = a[2][0];
entry1 = a[2][1];
entry2 = a[2][2];
temp[2][0] = entry0 * b[0][0] + entry1 * b[1][0] + entry2 * b[2][0];
temp[2][1] = entry0 * b[0][1] + entry1 * b[1][1] + entry2 * b[2][1];
temp[2][2] = entry0 * b[0][2] + entry1 * b[1][2] + entry2 * b[2][2];
// column 3
entry0 = a[3][0];
entry1 = a[3][1];
entry2 = a[3][2];
temp[3][0] = entry0 * b[0][0] + entry1 * b[1][0] + entry2 * b[2][0] + b[3][0];
temp[3][1] = entry0 * b[0][1] + entry1 * b[1][1] + entry2 * b[2][1] + b[3][1];
temp[3][2] = entry0 * b[0][2] + entry1 * b[1][2] + entry2 * b[2][2] + b[3][2];
temp[0][3] = temp[1][3] = temp[2][3] = 0;
temp[3][3] = 1;
mtxf_copy(dest, temp);
}
/**
* Set matrix 'dest' to 'mtx' scaled by vector s
*/
void mtxf_scale_vec3f(Mat4 dest, Mat4 mtx, Vec3f s) {
register s32 i;
for (i = 0; i < 4; i++) {
dest[0][i] = mtx[0][i] * s[0];
dest[1][i] = mtx[1][i] * s[1];
dest[2][i] = mtx[2][i] * s[2];
dest[3][i] = mtx[3][i];
}
}
/**
* Multiply a vector with a transformation matrix, which applies the transformation
* to the point. Note that the bottom row is assumed to be [0, 0, 0, 1], which is
* true for transformation matrices if the translation has a w component of 1.
*/
void mtxf_mul_vec3s(Mat4 mtx, Vec3s b) {
register f32 x = b[0];
register f32 y = b[1];
register f32 z = b[2];
b[0] = x * mtx[0][0] + y * mtx[1][0] + z * mtx[2][0] + mtx[3][0];
b[1] = x * mtx[0][1] + y * mtx[1][1] + z * mtx[2][1] + mtx[3][1];
b[2] = x * mtx[0][2] + y * mtx[1][2] + z * mtx[2][2] + mtx[3][2];
}
/**
* Convert float matrix 'src' to fixed point matrix 'dest'.
* The float matrix may not contain entries larger than 65536 or the console
* crashes. The fixed point matrix has entries with a 16-bit integer part, so
* the floating point numbers are multipled by 2^16 before being cast to a s32
* integer. If this doesn't fit, the N64 and iQue consoles will throw an
* exception. On Wii and Wii U Virtual Console the value will simply be clamped
* and no crashes occur.
*/
void mtxf_to_mtx(Mtx *dest, Mat4 src) {
#ifdef AVOID_UB
// Avoid type-casting which is technically UB by calling the equivalent
// guMtxF2L function. This helps little-endian systems, as well.
guMtxF2L(src, dest);
#else
s32 asFixedPoint;
register s32 i;
register s16 *a3 = (s16 *) dest; // all integer parts stored in first 16 bytes
register s16 *t0 = (s16 *) dest + 16; // all fraction parts stored in last 16 bytes
register f32 *t1 = (f32 *) src;
for (i = 0; i < 16; i++) {
asFixedPoint = *t1++ * (1 << 16); //! float-to-integer conversion responsible for PU crashes
*a3++ = GET_HIGH_S16_OF_32(asFixedPoint); // integer part
*t0++ = GET_LOW_S16_OF_32(asFixedPoint); // fraction part
}
#endif
}
/**
* Set 'mtx' to a transformation matrix that rotates around the z axis.
*/
void mtxf_rotate_xy(Mtx *mtx, s16 angle) {
Mat4 temp;
mtxf_identity(temp);
temp[0][0] = coss(angle);
temp[0][1] = sins(angle);
temp[1][0] = -temp[0][1];
temp[1][1] = temp[0][0];
mtxf_to_mtx(mtx, temp);
}
/**
* Extract a position given an object's transformation matrix and a camera matrix.
* This is used for determining the world position of the held object: since objMtx
* inherits the transformation from both the camera and Mario, it calculates this
* by taking the camera matrix and inverting its transformation by first rotating
* objMtx back from screen orientation to world orientation, and then subtracting
* the camera position.
*/
void get_pos_from_transform_mtx(Vec3f dest, Mat4 objMtx, Mat4 camMtx) {
f32 camX = camMtx[3][0] * camMtx[0][0] + camMtx[3][1] * camMtx[0][1] + camMtx[3][2] * camMtx[0][2];
f32 camY = camMtx[3][0] * camMtx[1][0] + camMtx[3][1] * camMtx[1][1] + camMtx[3][2] * camMtx[1][2];
f32 camZ = camMtx[3][0] * camMtx[2][0] + camMtx[3][1] * camMtx[2][1] + camMtx[3][2] * camMtx[2][2];
dest[0] =
objMtx[3][0] * camMtx[0][0] + objMtx[3][1] * camMtx[0][1] + objMtx[3][2] * camMtx[0][2] - camX;
dest[1] =
objMtx[3][0] * camMtx[1][0] + objMtx[3][1] * camMtx[1][1] + objMtx[3][2] * camMtx[1][2] - camY;
dest[2] =
objMtx[3][0] * camMtx[2][0] + objMtx[3][1] * camMtx[2][1] + objMtx[3][2] * camMtx[2][2] - camZ;
}
/**
* Take the vector starting at 'from' pointed at 'to' an retrieve the length
* of that vector, as well as the yaw and pitch angles.
* Basically it converts the direction to spherical coordinates.
*/
void vec3f_get_dist_and_angle(Vec3f from, Vec3f to, f32 *dist, s16 *pitch, s16 *yaw) {
register f32 x = to[0] - from[0];
register f32 y = to[1] - from[1];
register f32 z = to[2] - from[2];
*dist = sqrtf(x * x + y * y + z * z);
*pitch = atan2s(sqrtf(x * x + z * z), y);
*yaw = atan2s(z, x);
}
/**
* Construct the 'to' point which is distance 'dist' away from the 'from' position,
* and has the angles pitch and yaw.
*/
void vec3f_set_dist_and_angle(Vec3f from, Vec3f to, f32 dist, s16 pitch, s16 yaw) {
to[0] = from[0] + dist * coss(pitch) * sins(yaw);
to[1] = from[1] + dist * sins(pitch);
to[2] = from[2] + dist * coss(pitch) * coss(yaw);
}
/**
* Return the value 'current' after it tries to approach target, going up at
* most 'inc' and going down at most 'dec'.
*/
s32 approach_s32(s32 current, s32 target, s32 inc, s32 dec) {
//! If target is close to the max or min s32, then it's possible to overflow
// past it without stopping.
if (current < target) {
current += inc;
if (current > target) {
current = target;
}
} else {
current -= dec;
if (current < target) {
current = target;
}
}
return current;
}
/**
* Return the value 'current' after it tries to approach target, going up at
* most 'inc' and going down at most 'dec'.
*/
f32 approach_f32(f32 current, f32 target, f32 inc, f32 dec) {
if (current < target) {
current += inc;
if (current > target) {
current = target;
}
} else {
current -= dec;
if (current < target) {
current = target;
}
}
return current;
}
/**
* Helper function for atan2s. Does a look up of the arctangent of y/x assuming
* the resulting angle is in range [0, 0x2000] (1/8 of a circle).
*/
static u16 atan2_lookup(f32 y, f32 x) {
u16 ret;
if (x == 0) {
ret = gArctanTable[0];
} else {
ret = gArctanTable[(s32)(y / x * 1024 + 0.5f)];
}
return ret;
}
/**
* Compute the angle from (0, 0) to (x, y) as a s16. Given that terrain is in
* the xz-plane, this is commonly called with (z, x) to get a yaw angle.
*/
s16 atan2s(f32 y, f32 x) {
u16 ret;
if (x >= 0) {
if (y >= 0) {
if (y >= x) {
ret = atan2_lookup(x, y);
} else {
ret = 0x4000 - atan2_lookup(y, x);
}
} else {
y = -y;
if (y < x) {
ret = 0x4000 + atan2_lookup(y, x);
} else {
ret = 0x8000 - atan2_lookup(x, y);
}
}
} else {
x = -x;
if (y < 0) {
y = -y;
if (y >= x) {
ret = 0x8000 + atan2_lookup(x, y);
} else {
ret = 0xC000 - atan2_lookup(y, x);
}
} else {
if (y < x) {
ret = 0xC000 + atan2_lookup(y, x);
} else {
ret = -atan2_lookup(x, y);
}
}
}
return ret;
}
/**
* Compute the atan2 in radians by calling atan2s and converting the result.
*/
f32 atan2f(f32 y, f32 x) {
return (f32) atan2s(y, x) * M_PI / 0x8000;
}
#define CURVE_BEGIN_1 1
#define CURVE_BEGIN_2 2
#define CURVE_MIDDLE 3
#define CURVE_END_1 4
#define CURVE_END_2 5
/**
* Set 'result' to a 4-vector with weights corresponding to interpolation
* value t in [0, 1] and gSplineState. Given the current control point P, these
* weights are for P[0], P[1], P[2] and P[3] to obtain an interpolated point.
* The weights naturally sum to 1, and they are also always in range [0, 1] so
* the inteprolated point will never overshoot. The curve is guaranteed to go
* through the first and last point, but not through intermediate points.
*
* gSplineState ensures that the curve is clamped: the first two points
* and last two points have different weight formulas. These are the weights
* just before gSplineState transitions:
* 1: [1, 0, 0, 0]
* 1->2: [0, 3/12, 7/12, 2/12]
* 2->3: [0, 1/6, 4/6, 1/6]
* 3->3: [0, 1/6, 4/6, 1/6] (repeats)
* 3->4: [0, 1/6, 4/6, 1/6]
* 4->5: [0, 2/12, 7/12, 3/12]
* 5: [0, 0, 0, 1]
*
* I suspect that the weight formulas will give a 3rd degree B-spline with the
* common uniform clamped knot vector, e.g. for n points:
* [0, 0, 0, 0, 1, 2, ... n-1, n, n, n, n]
* TODO: verify the classification of the spline / figure out how polynomials were computed
*/
void spline_get_weights(Vec4f result, f32 t, UNUSED s32 c) {
f32 tinv = 1 - t;
f32 tinv2 = tinv * tinv;
f32 tinv3 = tinv2 * tinv;
f32 t2 = t * t;
f32 t3 = t2 * t;
switch (gSplineState) {
case CURVE_BEGIN_1:
result[0] = tinv3;
result[1] = t3 * 1.75f - t2 * 4.5f + t * 3.0f;
result[2] = -t3 * (11 / 12.0f) + t2 * 1.5f;
result[3] = t3 * (1 / 6.0f);
break;
case CURVE_BEGIN_2:
result[0] = tinv3 * 0.25f;
result[1] = t3 * (7 / 12.0f) - t2 * 1.25f + t * 0.25f + (7 / 12.0f);
result[2] = -t3 * 0.5f + t2 * 0.5f + t * 0.5f + (1 / 6.0f);
result[3] = t3 * (1 / 6.0f);
break;
case CURVE_MIDDLE:
result[0] = tinv3 * (1 / 6.0f);
result[1] = t3 * 0.5f - t2 + (4 / 6.0f);
result[2] = -t3 * 0.5f + t2 * 0.5f + t * 0.5f + (1 / 6.0f);
result[3] = t3 * (1 / 6.0f);
break;
case CURVE_END_1:
result[0] = tinv3 * (1 / 6.0f);
result[1] = -tinv3 * 0.5f + tinv2 * 0.5f + tinv * 0.5f + (1 / 6.0f);
result[2] = tinv3 * (7 / 12.0f) - tinv2 * 1.25f + tinv * 0.25f + (7 / 12.0f);
result[3] = t3 * 0.25f;
break;
case CURVE_END_2:
result[0] = tinv3 * (1 / 6.0f);
result[1] = -tinv3 * (11 / 12.0f) + tinv2 * 1.5f;
result[2] = tinv3 * 1.75f - tinv2 * 4.5f + tinv * 3.0f;
result[3] = t3;
break;
}
}
/**
* Initialize a spline animation.
* 'keyframes' should be an array of (s, x, y, z) vectors
* s: the speed of the keyframe in 1000/frames, e.g. s=100 means the keyframe lasts 10 frames
* (x, y, z): point in 3D space on the curve
* The array should end with three entries with s=0 (infinite keyframe duration).
* That's because the spline has a 3rd degree polynomial, so it looks 3 points ahead.
*/
void anim_spline_init(Vec4s *keyFrames) {
gSplineKeyframe = keyFrames;
gSplineKeyframeFraction = 0;
gSplineState = 1;
}
/**
* Poll the next point from a spline animation.
* anim_spline_init should be called before polling for vectors.
* Returns TRUE when the last point is reached, FALSE otherwise.
*/
s32 anim_spline_poll(Vec3f result) {
Vec4f weights;
s32 i;
s32 hasEnded = FALSE;
vec3f_copy(result, gVec3fZero);
spline_get_weights(weights, gSplineKeyframeFraction, gSplineState);
for (i = 0; i < 4; i++) {
result[0] += weights[i] * gSplineKeyframe[i][1];
result[1] += weights[i] * gSplineKeyframe[i][2];
result[2] += weights[i] * gSplineKeyframe[i][3];
}
if ((gSplineKeyframeFraction += gSplineKeyframe[0][0] / 1000.0f) >= 1) {
gSplineKeyframe++;
gSplineKeyframeFraction--;
switch (gSplineState) {
case CURVE_END_2:
hasEnded = TRUE;
break;
case CURVE_MIDDLE:
if (gSplineKeyframe[2][0] == 0) {
gSplineState = CURVE_END_1;
}
break;
default:
gSplineState++;
break;
}
}
return hasEnded;
}
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