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vec.h
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vec.h
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/*
mm_vec.h - zlib - Micha Mettke
ABOUT:
This is a ANSI C vector math library with header and implementations for
vector, matrix, plane, sphere and AABB math. Under normal circumstances it
is extremly awefull to use C for math since it does not allow to overload
operators. I noticed while writing one math libraries after another
that I had to change types and the implementation depending on the
different C versions (C89, C99 and C11).
Each version allows more control for example C99 has designated initializers
and C11 allows unamed unions inside structs. But since I do not want to
reimplement everything from scratch for each version I decided to make the
library work only on float arrays and therefore create a way to easily
generate the implementation independent of each vector, matrix,
plane, quaternion, sphere, AABB type. Downside is that it is not as nice to
use than directly defining types.
In general especially the vector library module fits as some kind of assembly
for code generation. Basically you write/use a lexer (like mm_lexer) and parse
operation like: c = a + b with a vec2 type and do a code generation pass before
compiling to generate xv_add(xv(c), xv(a), xv(b), 2) inside your file.
DEFINES:
MMX_IMPLEMENTATION
Generates the implementation of the library into the included file.
If not provided the library is in header only mode and can be included
in other headers or source files without problems. But only ONE file
should hold the implementation.
MMX_STATIC
The generated implementation will stay private inside implementation
file and all internal symbols and functions will only be visible inside
that file.
MMX_UINT32
MMX_UINT_PTR
If your compiler is C99 you do not need to define this.
Otherwise, mm_vec will try default assignments for them
and validate them at compile time. If they are incorrect, you will
get compile errors and will need to define them yourself.
MMX_MEMSET
You can define this to 'memset' or your own memset replacement.
If not, mm_vec.h uses a naive (maybe inefficent) implementation.
MMX_MEMCPY
You can define this to 'memcpy' or your own memcpy replacement.
If not, mm_vec.h uses a naive (maybe inefficent) implementation.
MMX_USE_DEGREES
If this is set all angles inside the library, input as well as output,
will be in degrees. Otherwise every angle will be in RAD.
MMX_SIN
MMX_FABS
MMX_COS
MMX_TAN
MMX_ASIN
MMX_ACOS
MMX_ATAN2
MMX_SQRT
Overrwrite these to use your own math functions. If not defined default
standard math library functions will be used
LICENSE: (zlib)
Copyright (c) 2015 Micha Mettke
This software is provided 'as-is', without any express or implied
warranty. In no event will the authors be held liable for any damages
arising from the use of this software.
Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it
freely, subject to the following restrictions:
1. The origin of this software must not be misrepresented; you must not
claim that you wrote the original software. If you use this software
in a product, an acknowledgment in the product documentation would be
appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be
misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
TESTED:
+ vector
+ matrix
USAGE:
This file behaves differently depending on what symbols you define
before including it.
Header-File mode:
If you do not define MMX_IMPLEMENTATION before including this file, it
will operate in header only mode. In this mode it declares all used structs
and the API of the library without including the implementation of the library.
Implementation mode:
If you define MMX_IMPLEMENTATIOn before including this file, it will
compile the implementation of the math library. To specify the visibility
as private and limit all symbols inside the implementation file
you can define MMX_STATIC before including this file.
Make sure that you only include this file implementation in *one* C or C++ file
to prevent collisions.
*/
/* ===============================================================
*
* HEADER
*
* =============================================================== */
#ifndef MMX_H_
#define MMX_H_
#ifdef __cplusplus
extern "C" {
#endif
#ifdef MMX_STATIC
#define MMX_API static
#else
#define MMX_API extern
#endif
#ifndef MMX_SQRT
#define MMX_SQRT sqrt
#endif
/* ---------------------------------------------------------------
* VECTOR
* ---------------------------------------------------------------*/
#define xv(v) ((float*)(&(v)))
#define xv_x(v) (v)[0]
#define xv_y(v) (v)[1]
#define xv_z(v) (v)[2]
#define xv_w(v) (v)[3]
#define xv_xx(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[0]
#define xv_xy(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[1]
#define xv_xz(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[2]
#define xv_xw(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[3]
#define xv_yx(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[0]
#define xv_yy(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[1]
#define xv_yz(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[2]
#define xv_yw(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[3]
#define xv_zx(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[0]
#define xv_zy(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[1]
#define xv_zz(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[2]
#define xv_zw(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[3]
#define xv_xxx(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[0], (t)[2] p (v)[0]
#define xv_xxy(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[0], (t)[2] p (v)[1]
#define xv_xxz(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[0], (t)[2] p (v)[2]
#define xv_xyx(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[1], (t)[2] p (v)[0]
#define xv_xyy(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[1], (t)[2] p (v)[1]
#define xv_xyz(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[1], (t)[2] p (v)[2]
#define xv_xzx(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[2], (t)[2] p (v)[0]
#define xv_xzy(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[2], (t)[2] p (v)[1]
#define xv_xzz(t,p,v) (t)[0] p (v)[0], (t)[1] p (v)[2], (t)[2] p (v)[2]
#define xv_yxx(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[0], (t)[2] p (v)[0]
#define xv_yxy(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[0], (t)[2] p (v)[1]
#define xv_yxz(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[0], (t)[2] p (v)[2]
#define xv_yyx(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[1], (t)[2] p (v)[0]
#define xv_yyy(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[1], (t)[2] p (v)[1]
#define xv_yyz(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[1], (t)[2] p (v)[2]
#define xv_yzx(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[2], (t)[2] p (v)[0]
#define xv_yzy(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[2], (t)[2] p (v)[1]
#define xv_yzz(t,p,v) (t)[0] p (v)[1], (t)[1] p (v)[2], (t)[2] p (v)[2]
#define xv_zxx(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[0], (t)[2] p (v)[0]
#define xv_zxy(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[0], (t)[2] p (v)[1]
#define xv_zxz(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[0], (t)[2] p (v)[2]
#define xv_zyx(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[1], (t)[2] p (v)[0]
#define xv_zyy(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[1], (t)[2] p (v)[1]
#define xv_zyz(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[1], (t)[2] p (v)[2]
#define xv_zzx(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[2], (t)[2] p (v)[0]
#define xv_zzy(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[2], (t)[2] p (v)[1]
#define xv_zzz(t,p,v) (t)[0] p (v)[2], (t)[1] p (v)[2], (t)[2] p (v)[2]
#define xv2_set(v,x,y) (v)[0]=(x), (v)[1]=(y)
#define xv3_set(v,x,y,z) (v)[0]=(x), (v)[1]=(y), (v)[2]=(z)
#define xv4_set(v,x,y,z,w) (v)[0]=(x), (v)[1]=(y), (v)[2]=(z), (v)[3]=(w)
#define xv2_zero(v) xv2_set(v,0,0)
#define xv3_zero(v) xv3_set(v,0,0,0)
#define xv4_zero(v) xv4_set(v,0,0,0,0)
#define xv2_cpy(to,from) (to)[0]=(from)[0], (to)[1]=(from)[1]
#define xv3_cpy(to,from) (to)[0]=(from)[0], (to)[1]=(from)[1], (to)[2]=(from)[2]
#define xv4_cpy(to,from) (to)[0]=(from)[0], (to)[1]=(from)[1],\
(to)[2]=(from)[2], (to)[3]=(from)[3]
#define xv_op(a,p,b,n, post) (((a)[n] p (b)[n]) post)
#define xv_applys(r,e,a,n,p,s,post) (r)[n] e ((((a)[n] p s)) post)
#define xv_expr(r,e,a,p,b,n,post) (r)[n] e ((xv_op(a,p,b,n,post)))
#define xv2_map(r,e,a,p,b,post)\
xv_expr(r,e,a,p,b,0,post),\
xv_expr(r,e,a,p,b,1,post)
#define xv3_map(r,e,a,p,b,post)\
xv_expr(r,e,a,p,b,0,post),\
xv_expr(r,e,a,p,b,1,post),\
xv_expr(r,e,a,p,b,2,post)
#define xv4_map(r,e,a,p,b,post)\
xv_expr(r,e,a,p,b,0,post),\
xv_expr(r,e,a,p,b,1,post),\
xv_expr(r,e,a,p,b,2,post),\
xv_expr(r,e,a,p,b,3,post)
#define xv2_apply(r,e,a,p,s,post)\
xv_applys(r,e,a,0,p,s,post),\
xv_applys(r,e,a,1,p,s,post)
#define xv3_apply(r,e,a,p,s,post)\
xv_applys(r,e,a,0,p,s,post),\
xv_applys(r,e,a,1,p,s,post),\
xv_applys(r,e,a,2,p,s,post)
#define xv4_apply(r,e,a,p,s,post)\
xv_applys(r,e,a,0,p,s,post),\
xv_applys(r,e,a,1,p,s,post),\
xv_applys(r,e,a,2,p,s,post),\
xv_applys(r,e,a,3,p,s,post)
#define vec2_eval(r,e,a,f)\
r[0]e(float)f(a[0]),\
r[1]e(float)f(a[1])
#define vec3_eval(r,e,a,f)\
r[0]e(float)f(a[0]),\
r[1]e(float)f(a[1]),\
r[2]e(float)f(a[2])
#define vec4_eval(r,e,a,f)\
r[0]e(float)f(a[0]),\
r[1]e(float)f(a[1]),\
r[2]e(float)f(a[2]),\
r[3]e(float)f(a[3])
#define vec2_eval2(r,e,a,b,f)\
r[0]e(float)f(a[0],b[0]),\
r[1]e(float)f(a[1],b[1])
#define vec3_eval2(r,e,a,b,f)\
r[0]e(float)f(a[0],b[0]),\
r[1]e(float)f(a[1],b[1]),\
r[2]e(float)f(a[1],b[2])
#define vec4_eval2(r,e,a,b,f)\
r[0]e(float)f(a[0],b[0]),\
r[1]e(float)f(a[1],b[1]),\
r[2]e(float)f(a[2],b[2]),\
r[3]e(float)f(a[3],b[3])
#define xv2_dot(a,b)\
xv_op(a,*,b,0,+0)+\
xv_op(a,*,b,1,+0)
#define xv3_dot(a,b)\
xv_op(a,*,b,0,+0)+\
xv_op(a,*,b,1,+0)+\
xv_op(a,*,b,2,+0)
#define xv4_dot(a,b)\
xv_op(a,*,b,0,+0)+\
xv_op(a,*,b,1,+0)+\
xv_op(a,*,b,2,+0)+\
xv_op(a,*,b,3,+0)
#define xv2_cross(r,a,b) (r) = (((a)[0] * (b)[1]) - ((a)[1]) * (b)[0])
#define xv4_cross(r, a, b) xv3_cross(r, a, b), (r)[3] = 1
#define xv_apply(r,e,a,p,s,dim) xv##dim##_apply(r,e,a,p,s,+0)
#define xv_map(r,e,a,p,b,dim) xv##dim##_map(r,e,a,p,b,+0)
#define xv_eval(r,e,f,a,dim) xv##dim##_eval(r,e,a,f)
#define xv_eval2(r,e,f,a,b,dim) xv##dim##_eval2(r,e,a,b,f)
#define xv_applyi(r,e,a,p,s,post,dim) xv##dim##_apply(r,e,a,p,s,post)
#define xv_mapi(r,e,a,p,b,post,dim) xv##dim##_map(r,e,a,p,b,post)
#define xv_add(r,a,b,dim) xv_map(r,=,a,+,b, dim)
#define xv_sub(r,a,b,dim) xv_map(r,=,a,-,b, dim)
#define xv_addeq(r,b,dim) xv_map(r,=,r,+,b, dim)
#define xv_subeq(r,b,dim) xv_map(r,=,r,-,b, dim)
#define xv_muli(r,a,s,dim) xv_apply(r,=,a,*,s,dim)
#define xv_divi(r,a,s,dim) xv_apply(r,=,a,/,s,dim)
#define xv_addi(r,a,s,dim) xv_apply(r,=,a,+,s,dim)
#define xv_subi(r,a,s,dim) xv_apply(r,=,a,-,s,dim)
#define xv_mulieq(r,s,dim) xv_apply(r,=,r,*,s,dim)
#define xv_divieq(r,s,dim) xv_apply(r,=,r,/,s,dim)
#define xv_addieq(r,s,dim) xv_apply(r,=,r,+,s,dim)
#define xv_subieq(r,s,dim) xv_apply(r,=,r,-,s,dim)
#define xv_addm(r,a,b,s,dim) xv_mapi(r,=,a,+,b,*s,dim)
#define xv_subm(r,a,b,s,dim) xv_mapi(r,=,a,-,b,*s,dim)
#define xv_addmeq(r,b,s,dim) xv_mapi(r,=,r,+,b,*s,dim)
#define xv_submeq(r,b,s,dim) xv_mapi(r,=,r,-,b,*s,dim)
#define xv_addd(r,a,b,s,dim) xv_mapi(r,=,a,+,b,/s,dim)
#define xv_subd(r,a,b,s,dim) xv_mapi(r,=,a,-,b,/s,dim)
#define xv_adddeq(r,b,s,dim) xv_mapi(r,=,r,+,b,/s,dim)
#define xv_subdeq(r,b,s,dim) xv_mapi(r,=,r,-,b,/s,dim)
#define xv_adda(r,a,b,s,dim) xv_mapi(r,=,a,+,b,+s,dim)
#define xv_suba(r,a,b,s,dim) xv_mapi(r,=,a,-,b,+s,dim)
#define xv_addaeq(r,b,s,dim) xv_mapi(r,=,r,+,b,+s,dim)
#define xv_subaeq(r,b,s,dim) xv_mapi(r,=,r,-,b,+s,dim)
#define xv_adds(r,a,b,s,dim) xv_mapi(r,=,a,+,b,-s,dim)
#define xv_subs(r,a,b,s,dim) xv_mapi(r,=,a,-,b,-s,dim)
#define xv_addseq(r,b,s,dim) xv_mapi(r,=,r,+,b,-s,dim)
#define xv_subseq(r,b,s,dim) xv_mapi(r,=,r,-,b,-s,dim)
#define xv_neg(r,a,dim) xv_applyi(r,=,a,*,-1.0f,+0,dim)
#define xv_dot(a,b,dim) xv##dim##_dot(a,b)
#define xv_len2(a,dim) xv##dim##_dot(a,a)
#define xv_len(a,dim) ((float)MMX_SQRT(xv_len2(a,dim)))
#define xv_len_inv(a,dim) xv_inv_sqrt(xv_len2(a,dim))
#define xv_cross(r,a,b,dim) xv##dim##_cross(r, a, b)
#define xv_lerp(r,a,t,b,dim)\
xv_apply(r,=,a,*,(1.0f - (t)),dim); xv_apply(r,+=,b,*,t, dim)
#define xv_norm(o, q, dim)do{\
float len_i_ = xv_len2(q,dim);\
if(len_i_ > 0.00001f){\
len_i_ = (float)MMX_SQRT(len_i_);\
len_i_ = 1.0f/len_i_;\
xv_muli(o, q, len_i_, dim);\
}}while(0)
#define xv_normeq(o, dim)do{\
float len_i_ = xv_len2(o,dim);\
if(len_i_ > 0.00001f){\
len_i_ = (float)MMX_SQRT(len_i_);\
len_i_ = 1.0f/len_i_;\
xv_mulieq(o, len_i_, dim);\
}}while(0)
#define xv_norm_len(len, o, q, dim)do{\
float len_i_ = xv_len2(q,dim);\
if(len_i_ > 0.00001f){\
len = (float)MMX_SQRT(len_i_);\
len_i_ = 1.0f/len;\
xv_muli(o, q, len_i_, dim);\
}}while(0)
#define xv_normeq_len(len, o, dim)do{\
float len_i_ = xv_len2(o,dim);\
if(len_i_ > 0.00001f){\
len = (float)MMX_SQRT(len_i_);\
len_i_ = 1.0f/len;\
xv_mulieq(o, len_i_, dim);\
}}while(0)
#define xv_norm_fast(o, q, dim)do{\
float len_i_ = xv_len2(q,dim);\
len_i_ = xv_inv_sqrt(len_i_);\
xv_muli(o, q, len_i_, dim);\
}}while(0)
#define xv_normeq_fast(o, dim)do{\
float len_i_ = xv_len2(o,dim);\
len_i_ = xv_inv_sqrt(len_i_);\
xv_mulieq(o, len_i_, dim);\
}}while(0)
#define xv_norm_len_fast(len, o, q, dim)do{\
float len_i_ = xv_len2(q,dim);\
float inv_len_i_ = xv_inv_sqrt(len_i_);\
xv_muli(o, q, inv_len_i_,dim);\
len = len_i_ * inv_len_i;\
}}while(0)
#define xv_normeq_len_fast(len, o, dim)do{\
float len_i_ = xv_len2(o,dim);\
float inv_len_i_ = xv_inv_sqrt(len_i_);\
xv_mulieq(o, inv_len_i_,dim);\
len = len_i_ * inv_len_i;\
}}while(0)
MMX_API float xv_inv_sqrt(float n);
MMX_API float xv3_angle(float *axis, const float *a, const float *b);
MMX_API void xv3_cross(float *result, const float *v1, const float *v2);
MMX_API void xv3_slerp(float *r, const float *a, float t, const float *b);
MMX_API void xv3_project_to_sphere(float *r, const float *v, float radius);
MMX_API void xv3_project_to_plane(float *r, const float *v, const float *normal,
float over_bounce);
MMX_API int xv3_project_along_plane(float *r, const float *v, const float *normal,
float epsilon, float over_bounce);
MMX_API void xv3_project(float *res3, const float *obj3, const float *mat4_model,
const float *mat4_proj, float *viewport4);
MMX_API void xv3_unproject(float *res3, const float *window3, const float *mat4_model,
const float *mat4_proj, const float *viewport4);
/* ---------------------------------------------------------------
* MATRIX
* ---------------------------------------------------------------*/
#define XM_AXIS_X 0
#define XM_AXIS_Y 1
#define XM_AXIS_Z 2
#define xm(m) ((float*)&(m))
MMX_API void xm2_identity(float *m);
MMX_API void xm2_transpose(float *m);
MMX_API void xm2_mul(float *product, const float *a, const float *b);
MMX_API void xm2_transform(float *r, const float *m, const float *v);
MMX_API void xm2_rotate(float *m, float angle);
MMX_API void xm2_scale(float *m, float x, float y);
MMX_API float xm2_determinant(const float *m);
MMX_API int xm2_inverse_self(float *m);
MMX_API int xm2_inverse(float *r, const float *m);
MMX_API void xm3_identity(float *out);
MMX_API void xm3_transpose(float *out);
MMX_API void xm3_mul(float *out, const float *a, const float *b);
MMX_API void xm3_scale(float *out, float x, float y, float z);
MMX_API void xm3_transform(float *out, const float *m, const float *v);
MMX_API void xm3_rotate(float *out, float angle, float X, float Y, float Z);
MMX_API void xm3_rotate_x(float *out, float angle);
MMX_API void xm3_rotate_y(float *out, float angle);
MMX_API void xm3_rotate_z(float *out, float angle);
MMX_API void xm3_rotate_axis(float *out, int axis, float angle);
MMX_API void xm3_rotate_align(float *out, const float *dest, const float *src);
MMX_API void xm3_rotate_vector(float *out, const float *in, float angle, float X, float Y, float Z);
MMX_API float xm3_determinant(const float *m);
MMX_API int xm3_inverse_self(float *self);
MMX_API int xm3_inverse(float *out, const float *in);
MMX_API void xm3_from_quat(float *out, const float *quat_input);
MMX_API void xm3_from_mat4(float *out, const float *mat3_input);
MMX_API void xm4_identity(float *self);
MMX_API void xm4_transpose(float *self);
MMX_API void xm4_translate(float *out, const float *d);
MMX_API void xm4_translatev(float *out, float x, float y, float z);
MMX_API void xm4_scale(float *out, const float *scale);
MMX_API void xm4_scalev(float *out, float x, float y, float z);
MMX_API void xm4_rotate(float *out, float angle, const float *axis);
MMX_API void xm4_rotatef(float *out, float angle, float X, float Y, float Z);
MMX_API void xm4_rotate_x(float *out, float angle);
MMX_API void xm4_rotate_y(float *out, float angle);
MMX_API void xm4_rotate_z(float *out, float angle);
MMX_API void xm4_rotate_axis(float *out, int axis, float angle);
MMX_API void xm4_mul(float *out, const float *a, const float *b);
MMX_API float xm4_determinant(const float *m);
MMX_API int xm4_inverse_self(float *self);
MMX_API int xm4_inverse(float *out, const float *in);
MMX_API void xm4_transform(float *out, const float *matrix, const float *in);
MMX_API void xm4_ortho(float *out, float left, float right, float bottom, float top);
MMX_API void xm4_orthographic(float *out, float left, float right, float bottom, float top, float near, float far);
MMX_API void xm4_frustum(float *out, float left, float right, float buttom, float top, float near, float far);
MMX_API void xm4_persp(float *out, float fov, float aspect, float near, float far);
MMX_API void xm4_lookat(float *out, const float *eye, const float *center, const float *up);
MMX_API void xm4_from_quat(float *out, const float *quat_input);
MMX_API void xm4_from_quat_vec(float *out, const float *quat_input, const float *position);
MMX_API void xm4_from_mat3(float *out, const float *matrix3);
/* ---------------------------------------------------------------
* QUATERNION
* ---------------------------------------------------------------*/
#define xq(q) ((float*)&(q))
#define xq_set(q, x,y,z,w) xv4_set(q,x,y,z,w)
#define xq_cpy(to, from) xv4_cpy(to,from)
MMX_API void xq_from_mat3(float *quat, const float *mat3);
MMX_API void xq_from_euler(float *q, float pitch, float yaw, float roll);
MMX_API void xq_rotation(float *quat, float angle, const float *vec3_axis);
MMX_API void xq_rotationf(float *quat, float angle, float x, float y, float z);
MMX_API void xq_rotation_from_to(float *quat, const float *from_vec3, const float *to_vec3);
MMX_API void xq_transform(float *out, const float *q, const float *v);
MMX_API void xq_mul(float *out, const float *a, const float *b);
MMX_API void xq_integrate2D(float *out, const float *q, float *omega, float delta);
MMX_API void xq_integrate3D(float *out, const float *q, float *omega3, float delta);
MMX_API float xq_invert(float *out, const float *in);
MMX_API float xq_inverteq(float *self);
MMX_API float xq_get_rotation(float *axis_output, const float *quat);
MMX_API float xq_get_rotation_in_axis(float *res, int axis, const float *q);
MMX_API void xq_get_euler(float *pitch, float *yaw, float *roll, const float *quat);
#define xq_identity(q) (q)[0] = (q)[1] = (q)[2] = 0, (q)[3] = 1.0f
#define xq_conjugate(t,f) ((t)[0] = -(f)[0],(t)[1] = -(f)[1],(t)[2] = -(f)[2], (t)[3] = (f)[3])
#define xq_norm(o, q) xv_norm(o, q, 4)
#define xq_normeq(q) xv_normeq(q, 4)
#define xq_norm_len(len, o, q) xv_norm_len(len, o, q, 4)
#define xq_normeq_len(len, q) xv_normeq_len(len, q, 4)
#define xq_len(q) xv_len(q, 4)
#define xq_add(r, a, b) xv_add(r, a, b, 4)
#define xq_sub(r, a, b) xv_sub(r, a, b, 4)
#define xq_addeq(r, b) xv_addeq(r, b, 4)
#define xq_subeq(r, b) xv_subeq(r, b, 4)
#define xq_muli(r, a, s) xv_muli(r, a, s, 4)
#define xq_divi(r, a, s) xv_divi(r, a, s, 4)
#define xq_mulieq(r, s) xv_mulieq(r, s, 4)
#define xq_divieq(r, s) xv_divieq(r, s, 4)
#ifdef __cplusplus
}
#endif
#endif /* MMX_H_ */
/* ===============================================================
*
* IMPLEMENTATION
*
* ===============================================================*/
#ifdef MMX_IMPLEMENTATION
#define MMX_INTERN static
#define MMX_GLOBAL static
#define MMX_STORAGE static
#define MMX_MIN(a,b) (((a)<(b))?(a):(b))
#define MMX_MAX(a,b) (((a)>(b))?(a):(b))
#define MMX_DEG2RAD(a) ((a)*(MMX_PI/180.0f))
#define MMX_RAD2DEG(a) ((a)*(180.0f/MMX_PI))
#define MMX_MIN(a,b) (((a)<(b))?(a):(b))
#define MMX_MAX(a,b) (((a)>(b))?(a):(b))
#define MMX_CLAMP(a,v, b) MMX_MIN(b, MMX_MAX(a,v))
#ifndef MMX_SIN
#define MMX_SIN sin
#endif
#ifndef MMX_FABS
#define MMX_FABS fabs
#endif
#ifndef MMX_COS
#define MMX_COS cos
#endif
#ifndef MMX_TAN
#define MMX_TAN tan
#endif
#ifndef MMX_ASIN
#define MMX_ASIN asin
#endif
#ifndef MMX_ACOS
#define MMX_ACOS acos
#endif
#ifndef MMX_ATAN2
#define MMX_ATAN2 atan2
#endif
#ifndef MMX_PI
#define MMX_PI 3.141592654f
#endif
#ifndef MMX_MATRIX_EPISLON
#define MMX_MATRIX_EPISLON 1e-6
#endif
#ifndef MMX_MATRIX_INVERSE_EPISLON
#define MMX_MATRIX_INVERSE_EPISLON 1e-14
#endif
#ifndef MMX_MEMSET
#define MMX_MEMSET xv_memset
#endif
#ifndef MMX_MEMCPY
#define MMX_MEMCPY xv_memcpy
#endif
/* ---------------------------------------------------------------
*
* UTIL
*
* ---------------------------------------------------------------*/
MMX_API float
xv_inv_sqrt(float number)
{
float x2;
const float threehalfs = 1.5f;
union {unsigned long i; float f;} conv;
conv.i = 0; /* I am not sure what happens if sizeof(i) > sizeof(float) so zero */
conv.f = number;
x2 = number * 0.5f;
conv.i = 0x5f375A84 - (conv.i >> 1);
conv.f = conv.f * (threehalfs - (x2 * conv.f * conv.f));
return conv.f;
}
MMX_API void
xv3_cross(float *result, const float *v1, const float *v2)
{
float v1x = v1[0], v1y = v1[1], v1z = v1[2];
float v2x = v2[0], v2y = v2[1], v2z = v2[2];
result[0] = (v1y * v2z) - (v1z * v2y);
result[1] = (v1z * v2x) - (v1x * v2z);
result[2] = (v1x * v2y) - (v1y * v2x);
}
static void*
xv_memcpy(void *dst0, const void *src0, int size)
{
int i;
for (i = 0; i < size; ++i)
*((char*)dst0 + i) = *((const char*)src0 + i);
return dst0;
}
MMX_INTERN void
xv_memset(void *ptr, int c0, int size)
{
int i;
for (i = 0; i < size; ++i)
*((char*)ptr + i) = (char)c0;
}
#define xv_zero_struct(s) xv_zero_size(&s, (int)sizeof(s))
#define xv_zero_array(p,n) xv_zero_size(p, (n) * (int)sizeof((p)[0]))
MMX_INTERN void
xv_zero_size(void *ptr, int size)
{
MMX_MEMSET(ptr, 0, size);
}
/* ---------------------------------------------------------------
*
* VECTOR
*
* ---------------------------------------------------------------*/
MMX_API float
xv3_angle(float *axis, const float *a, const float *b)
{
float d;
float angle;
xv_cross(axis, a, b, 3);
xv_normeq(axis, 3);
d = xv_dot(a, b, 3);
angle = (float)MMX_ACOS(MMX_CLAMP(-1.0f, d, 1.0f));
#ifdef MMX_USE_DEGREES
angle = MMX_RAD2DEG(angle);
#endif
return angle;
}
MMX_API void
xv3_slerp(float *r, const float *a, float t, const float *b)
{
float t0[3], t1[3];
float omega, cosom, sinom, scale0, scale1;
if (t <= 0.0f) {
r[0] = a[0];
r[1] = a[1];
r[2] = a[2];
return;
} else if (t >= 1.0f) {
r[0] = b[0];
r[1] = b[1];
r[2] = b[2];
return;
}
cosom = xv_dot(a,b,3);
if ((1.0f - cosom) > 1e-6) {
omega = (float)MMX_ACOS(cosom);
sinom = (float)MMX_SIN(omega);
scale0 = (float)MMX_SIN((1.0f - t) * omega)/sinom;
scale1 = (float)MMX_SIN(t*omega)/sinom;
} else {
scale0 = 1.0f - t;
scale1 = t;
}
xv_muli(t0, a, scale0, 3);
xv_muli(t1, b, scale1, 3);
xv_add(r, t0, t1, 3);
}
MMX_API void
xv3_project_to_sphere(float *r, const float *v, float radius)
{
float rsqr = radius * radius;
float len = xv_len(v, 3);
r[0] = v[0]; r[1] = v[1];
if (len < rsqr *0.5f)
r[2] = (float)MMX_SQRT(rsqr - len);
else r[3] = rsqr / (2.0f * (float)MMX_SQRT(len));
}
MMX_API void
xv3_project_to_plane(float *r, const float *v, const float *normal, float over_bounce)
{
float t[3];
float backoff = xv_dot(v, normal, 3);
if (over_bounce != 1.0f) {
if (backoff < 0.0f)
backoff *= over_bounce;
else backoff /= over_bounce;
}
xv_muli(t, normal, backoff, 3);
xv_sub(r, v, t, 3);
}
MMX_API int
xv3_project_along_plane(float *r, const float *v, const float *normal,
const float epsilon, float over_bounce)
{
float len, temp;
float t[3], cross[3];
xv_cross(t, v, normal, 3);
xv_cross(cross, t, v, 3);
xv_normeq(cross, 3);
len = xv_dot(normal, cross, 3);
len = (len < 0.0f) ? -len : len;
if (len < epsilon)
return 0;
temp = (over_bounce * xv_dot(normal, v, 3)) / len;
xv_mulieq(cross, temp, 3);
xv_sub(r, v, cross, 3);
return 1;
}
MMX_API void
xv3_project(float *res3, const float *obj3, const float *mat_model,
const float *mat_proj, float *viewport)
{
float tmp[4];
xv3_cpy(tmp, obj3);
tmp[3] = 1.0f;
xm4_transform(tmp, mat_model, tmp);
xm4_transform(tmp, mat_proj, tmp);
xv_divieq(tmp, tmp[3], 4);
xv_mulieq(tmp, 0.5f, 4);
xv_addieq(tmp, 0.5f, 4);
tmp[0] = tmp[0] * (viewport[2] + viewport[0]);
tmp[1] = tmp[1] * (viewport[3] + viewport[1]);
xv3_cpy(res3, tmp);
}
MMX_API void
xv3_unproject(float *res3, const float *win, const float *mat_view,
const float *mat_proj, const float *viewport)
{
float inverse[16], tmp[4];
xm4_mul(inverse, mat_view, mat_proj);
xm4_inverse_self(inverse);
xv4_set(tmp, win[0], win[1], win[2], 1.0f);
tmp[0] = (tmp[0] - viewport[0]) / viewport[2];
tmp[1] = (tmp[1] - viewport[1]) / viewport[3];
xv_mulieq(tmp, 2, 4);
xv_subieq(tmp, 1, 4);
xm4_transform(tmp, inverse, tmp);
xv_divi(res3, tmp, tmp[3], 3);
}
/* ---------------------------------------------------------------
*
* MATRIX
*
* ---------------------------------------------------------------*/
MMX_API void
xm2_identity(float *m)
{
#define M(col, row) m[(col<<1)+row]
M(0,0) = 1.0f; M(0,1) = 0.0f;
M(0,0) = 0.0f; M(0,1) = 1.0f;
#undef M
}
MMX_API void
xm2_transpose(float *m)
{
#define M(col, row) m[(col<<1)+row]
float temp = M(0,1);
M(0,1) = M(1,0);
M(1,0) = temp;
#undef M
}
MMX_API void
xm2_mul(float *product, const float *m1, const float *m2)
{
#define A(col, row) a[(col<<1)+row]
#define B(col, row) b[(col<<1)+row]
#define P(col, row) o[(col<<1)+row]
/* load */
float a[4], b[4], o[4];
MMX_MEMCPY(a, m1, sizeof(a));
MMX_MEMCPY(b, m2, sizeof(b));
/* calculate */
P(0,0) = A(0,0) * B(0,0) + A(0,1) * B(1,0);
P(0,1) = A(0,0) * B(0,1) + A(0,1) * B(1,1);
P(1,0) = A(1,0) * B(0,0) + A(1,1) * B(1,0);
P(1,1) = A(1,0) * B(0,1) + A(1,1) * B(1,1);
/* store */
MMX_MEMCPY(product, o, sizeof(o));
#undef A
#undef B
#undef P
}
MMX_API void
xm2_transform(float *r, const float *m, const float *vec)
{
float v[2], o[2];
#define X(a) a[0]
#define Y(a) a[1]
#define M(col, row) m[(col<<1)+row]
xv2_cpy(v, vec);
X(o) = M(0,0)*X(v) + M(0,1)*Y(v);
Y(o) = M(1,0)*X(v) + M(1,1)*Y(v);
xv2_cpy(r, o);
#undef X
#undef Y
#undef M
}
MMX_API void
xm2_rotate(float *m, float angle)
{
#define M(col, row) m[(col<<1)+row]
#ifdef MMX_USE_DEGREES
float s = (float)MMX_SIN(MMX_DEG2RAD(angle));
float c = (float)MMX_COS(MMX_DEG2RAD(angle));
#else
float s = (float)MMX_SIN(angle);
float c = (float)MMX_COS(angle);
#endif
if (angle >= 0) {
M(0,0) = c; M(0,1) = s;
M(1,0) = -s; M(1,1) = c;
} else {
M(0,0) = c; M(0,1) = -s;
M(1,0) = s; M(1,1) = c;
}
#undef M
}
MMX_API void
xm2_scale(float *m, float x, float y)
{
#define M(col, row) m[(col<<1)+row]
M(0,0) = x; M(0,1) = 0;
M(0,0) = 0; M(0,1) = y;
#undef M
}
MMX_API float
xm2_determinant(const float *m)
{
#define M(col, row) m[(col<<1)+row]
return M(0,0) * M(1,1) - M(0,1) * M(1,0);
#undef M
}
MMX_API int
xm2_inverse_self(float *m)
{
#define M(col, row) m[(col<<1)+row]
float det, inv_det, a;
det = M(0,0) * M(1,1) - M(0,1) * M(1,0);
if (MMX_FABS(det) < MMX_MATRIX_INVERSE_EPISLON)
return 0;
inv_det = 1.0f/det;
a = M(0,0);
M(0,0) = M(1,1) * inv_det;
M(0,1) = -M(0,1) * inv_det;
M(1,0) = -M(1,0) * inv_det;
M(1,1) = a * inv_det;
#undef M
return 1;
}
MMX_API int
xm2_inverse(float *r, const float *m)
{
MMX_MEMCPY(r, m, sizeof(float) * 4);
return xm2_inverse_self(r);
}
MMX_API void
xm3_identity(float *m)
{
#define M(col, row) m[(col*3)+row]
M(0,0) = 1.0f; M(0,1) = 0.0f; M(0,2) = 0.0f;
M(1,0) = 0.0f; M(1,1) = 1.0f; M(1,2) = 0.0f;
M(2,0) = 0.0f; M(2,1) = 0.0f; M(2,2) = 1.0f;
#undef M
}
MMX_API void
xm3_transpose(float *m)
{
int i, j;
#define M(col, row) m[(col*3)+row]
for (j = 0; j < 3; ++j) {
for (i = j+1; i < 3; ++i) {
float t = M(i,j);
M(i,j) = M(j,i);
M(j,i) = t;
}
}
#undef M
}
MMX_API void
xm3_rotate_x(float *m, float angle)
{
#ifdef MMX_USE_DEGREES
float s = (float)MMX_SIN(MMX_DEG2RAD(angle));
float c = (float)MMX_COS(MMX_DEG2RAD(angle));
#else
float s = (float)MMX_SIN(angle);
float c = (float)MMX_COS(angle);
#endif
#define M(col, row) m[(col*3)+row]
M(0,0) = 1; M(0,1) = 0; M(0,2) = 0;
M(1,0) = 0; M(1,1) = c; M(1,2) =-s;
M(2,0) = 0; M(2,1) = s; M(2,2) = c;
#undef M
}
MMX_API void
xm3_rotate_y(float *m, float angle)
{
#ifdef MMX_USE_DEGREES
float s = (float)MMX_SIN(MMX_DEG2RAD(angle));
float c = (float)MMX_COS(MMX_DEG2RAD(angle));
#else
float s = (float)MMX_SIN(angle);
float c = (float)MMX_COS(angle);
#endif
#define M(col, row) m[(col*3)+row]
M(0,0) = c; M(0,1) = 0; M(0,2) = s;
M(1,0) = 0; M(1,1) = 1; M(1,2) = 0;
M(2,0) =-s; M(2,1) = 0; M(2,2) = c;
#undef M
}
MMX_API void
xm3_rotate_z(float *m, float angle)
{
#ifdef MMX_USE_DEGREES
float s = (float)MMX_SIN(MMX_DEG2RAD(angle));
float c = (float)MMX_COS(MMX_DEG2RAD(angle));
#else
float s = (float)MMX_SIN(angle);
float c = (float)MMX_COS(angle);
#endif
#define M(col, row) m[(col*3)+row]
M(0,0) = c; M(0,1) =-s; M(0,2) = 0;
M(1,0) = s; M(1,1) = c; M(1,2) = 0;
M(2,0) = 0; M(2,1) = 0; M(2,2) = 1;
#undef M
}
MMX_API void
xm3_rotate_axis(float *m, int axis, float angle)
{
switch (axis) {
case XM_AXIS_X: xm3_rotate_x(m, angle); break;
case XM_AXIS_Y: xm3_rotate_y(m, angle); break;
case XM_AXIS_Z: xm3_rotate_z(m, angle); break;
default: xm3_identity(m); break;
}
}
MMX_API void
xm3_rotate(float *m, float angle, float X, float Y, float Z)
{
#define M(col, row) m[(col*3)+row]
#ifdef MMX_USE_DEGREES
float s = (float)MMX_SIN(MMX_DEG2RAD(angle));
float c = (float)MMX_COS(MMX_DEG2RAD(angle));
#else
float s = (float)MMX_SIN(angle);
float c = (float)MMX_COS(angle);
#endif
float oc = 1.0f - c;
M(0,0) = oc * X * X + c;
M(0,1) = oc * X * Y - Z * s;
M(0,2) = oc * Z * X + Y * s;
M(1,0) = oc * X * Y + Z * s;