sm64

math_util.c (26792B)

---

 #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
 
 #ifdef __GNUC__
 #if defined(__clang__)
   #pragma GCC diagnostic ignored "-Wreturn-stack-address"
 #else
   #pragma GCC diagnostic ignored "-Wreturn-local-addr"
 #endif
 #endif
 
 /// 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
 }
 
 /// 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
 }
 
 /// Subtract vector a from 'dest'
 void *vec3s_sub(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
 }
 
 /// 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
 }
 
 #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;
     // These loops must be one line to match on -O2
 
     // 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 multiplied 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 interpolated 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;
 }