Rafael Barreto
d1f4c1fd83
git-svn-id: svn://svn.code.sf.net/p/actiongame/code/trunk/ac@5655 e016b1c5-ed68-44aa-a2f7-31cac88cffde
377 lines
11 KiB
C++
377 lines
11 KiB
C++
// Fast Inverse Sqrt
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// http://www.gamedev.net/community/forums/topic.asp?topic_id=139956
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// http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf
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// http://www.mceniry.net/papers/Fast%20Inverse%20Square%20Root.pdf
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// http://en.wikipedia.org/wiki/Fast_inverse_square_root
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#define UFINVSQRT(x) union { int d; float f; } u; u.f = x; u.d = 0x5f3759df - (u.d >> 1)
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inline float ufInvSqrt (float x) { UFINVSQRT(x); return u.f; } // about 3.5% of error
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inline float fInvSqrt (float x) { UFINVSQRT(x); return 0.5f * u.f * ( 3.00175f - x * u.f * u.f ); } // about 0.1% of error
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inline float fSqrt (float x) { return x * fInvSqrt(x); }
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inline float ufSqrt (float x) { return x * ufInvSqrt(x); }
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inline float fACos( float x )
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{
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int s = 1;
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float y, r = 0;
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if ( x < 0 )
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{
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s = -1;
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r = 2.0f;
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y = 1.0f + x;
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}
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else y = 1.0f - x;
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UFINVSQRT(y);
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u.f = 0.5f * u.f * ( 3.0f - y * u.f * u.f );
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u.f = y * 0.5f * u.f * ( 3.0f - y * u.f * u.f );
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return 1.57079632f * ( r + s * u.f * ( 0.9003163f + y * ( 0.07782684f + y * ( 0.006777598f + y * 0.015079262f ) ) ) );
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}
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#undef UFINVSQRT
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inline float pow2(float x)
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{
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return x*x;
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}
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// Fast Cosine
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// inspired after http://www.devmaster.net/forums/showthread.php?t=5784
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#define FCOS \
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x = fabs(x); \
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int s = 1; \
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if ( x > 1.0f ) \
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{ \
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int n = 0.5f * ( x + 1.0f ); \
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x -= 2 * n; \
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s = 1 - 2 * (n%2); \
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} \
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float y = ( 1.0f - x*x ); \
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return s * y * ( 0.7853982f + y * 0.2146018f )
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inline float fCos(float x) { x *= 0.636619772f; FCOS; }
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inline float fSin(float x) { x *= 0.636619772f; x -= 1.0f; FCOS; }
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#undef FCOS
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inline float ufS2C(float x) { x *= x; return x < 1.0f ? ufSqrt(1.0f - x) : 0.0f; }
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struct vec
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{
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union
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{
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struct { float x, y, z; };
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float v[3];
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int i[3];
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};
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vec() {x=y=z=0;}
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vec(float a, float b, float c) : x(a), y(b), z(c) {}
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vec(float *v) : x(v[0]), y(v[1]), z(v[2]) {}
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float &operator[](int i) { return v[i]; }
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float operator[](int i) const { return v[i]; }
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bool iszero() const { return x==0 && y==0 && z==0; }
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bool operator==(const vec &o) const { return x == o.x && y == o.y && z == o.z; }
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bool operator!=(const vec &o) const { return x != o.x || y != o.y || z != o.z; }
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vec operator-() const { return vec(-x, -y, -z); }
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vec &mul(float f) { x *= f; y *= f; z *= f; return *this; }
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vec &div(float f) { x /= f; y /= f; z /= f; return *this; }
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vec &add(float f) { x += f; y += f; z += f; return *this; }
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vec &sub(float f) { x -= f; y -= f; z -= f; return *this; }
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vec &add(const vec &o) { x += o.x; y += o.y; z += o.z; return *this; }
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vec &sub(const vec &o) { x -= o.x; y -= o.y; z -= o.z; return *this; }
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float squaredlen() const { return x*x + y*y + z*z; }
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float sqrxy() const { return x*x + y*y; }
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float dot(const vec &o) const { return x*o.x + y*o.y + z*o.z; }
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float dotxy(const vec &o) const { return x*o.x + y*o.y; }
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float magnitude() const { return sqrtf(squaredlen()); }
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vec &normalize() { div(magnitude()); return *this; }
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float fmag() const { return fSqrt(squaredlen()); }
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float ufmag() const { return ufSqrt(squaredlen()); }
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float dist(const vec &e) const { vec t; return dist(e, t); }
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float dist(const vec &e, vec &t) const { t = *this; t.sub(e); return t.magnitude(); }
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float distxy(const vec &e) const { float dx = e.x - x, dy = e.y - y; return sqrtf(dx*dx + dy*dy); }
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float magnitudexy() const { return sqrtf(x*x + y*y); }
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float fmagxy() const { return fSqrt(x*x + y*y); }
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float ufmagxy() const { return ufSqrt(x*x + y*y); }
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bool reject(const vec &o, float max) const { return x>o.x+max || x<o.x-max || y>o.y+max || y<o.y-max; }
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vec &cross(const vec &a, const vec &b) { x = a.y*b.z-a.z*b.y; y = a.z*b.x-a.x*b.z; z = a.x*b.y-a.y*b.x; return *this; }
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float cxy(const vec &a) { return x*a.y-y*a.x; }
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void rotate_around_z(float angle) { *this = vec(cosf(angle)*x-sinf(angle)*y, cosf(angle)*y+sinf(angle)*x, z); }
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void rotate_around_x(float angle) { *this = vec(x, cosf(angle)*y-sinf(angle)*z, cosf(angle)*z+sinf(angle)*y); }
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void rotate_around_y(float angle) { *this = vec(cosf(angle)*x-sinf(angle)*z, y, cosf(angle)*z+sinf(angle)*x); }
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vec &rotate(float angle, const vec &d)
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{
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float c = cosf(angle), s = sinf(angle);
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return rotate(c, s, d);
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}
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vec &rotate(float c, float s, const vec &d)
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{
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*this = vec(x*(d.x*d.x*(1-c)+c) + y*(d.x*d.y*(1-c)-d.z*s) + z*(d.x*d.z*(1-c)+d.y*s),
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x*(d.y*d.x*(1-c)+d.z*s) + y*(d.y*d.y*(1-c)+c) + z*(d.y*d.z*(1-c)-d.x*s),
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x*(d.x*d.z*(1-c)-d.y*s) + y*(d.y*d.z*(1-c)+d.x*s) + z*(d.z*d.z*(1-c)+c));
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return *this;
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}
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void orthogonal(const vec &d)
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{
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int i = fabs(d.x) > fabs(d.y) ? (fabs(d.x) > fabs(d.z) ? 0 : 2) : (fabs(d.y) > fabs(d.z) ? 1 : 2);
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v[i] = d[(i+1)%3];
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v[(i+1)%3] = -d[i];
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v[(i+2)%3] = 0;
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}
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};
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static inline bool htcmp(const vec &x, const vec &y)
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{
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return x == y;
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}
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static inline uint hthash(const vec &k)
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{
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return k.i[0]^k.i[1]^k.i[2];
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}
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struct vec4
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{
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union
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{
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struct { float x, y, z, w; };
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float v[4];
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};
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vec4() {}
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explicit vec4(const vec &p, float w = 0) : x(p.x), y(p.y), z(p.z), w(w) {}
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vec4(float x, float y, float z, float w) : x(x), y(y), z(z), w(w) {}
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float &operator[](int i) { return v[i]; }
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float operator[](int i) const { return v[i]; }
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};
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struct ivec
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{
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union
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{
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struct { int x, y, z; };
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int v[3];
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};
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ivec() {}
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ivec(const vec &v) : x(int(v.x)), y(int(v.y)), z(int(v.z)) {}
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ivec(int a, int b, int c) : x(a), y(b), z(c) {}
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vec tovec() const { return vec(x, y, z); }
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int &operator[](int i) { return v[i]; }
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int operator[](int i) const { return v[i]; }
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bool operator==(const ivec &v) const { return x==v.x && y==v.y && z==v.z; }
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bool operator!=(const ivec &v) const { return x!=v.x || y!=v.y || z!=v.z; }
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ivec &mul(int n) { x *= n; y *= n; z *= n; return *this; }
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ivec &div(int n) { x /= n; y /= n; z /= n; return *this; }
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ivec &add(int n) { x += n; y += n; z += n; return *this; }
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ivec &sub(int n) { x -= n; y -= n; z -= n; return *this; }
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ivec &add(const ivec &v) { x += v.x; y += v.y; z += v.z; return *this; }
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ivec &sub(const ivec &v) { x -= v.x; y -= v.y; z -= v.z; return *this; }
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ivec &mask(int n) { x &= n; y &= n; z &= n; return *this; }
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ivec &cross(const ivec &a, const ivec &b) { x = a.y*b.z-a.z*b.y; y = a.z*b.x-a.x*b.z; z = a.x*b.y-a.y*b.x; return *this; }
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int dot(const ivec &o) const { return x*o.x + y*o.y + z*o.z; }
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};
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static inline bool htcmp(const ivec &x, const ivec &y)
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{
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return x == y;
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}
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static inline uint hthash(const ivec &k)
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{
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return k.x^k.y^k.z;
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}
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struct bvec
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{
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union
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{
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struct { uchar x, y, z; };
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uchar v[3];
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};
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bvec() {}
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bvec(uchar x, uchar y, uchar z) : x(x), y(y), z(z) {}
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bvec(const vec &v) : x((uchar)((v.x+1)*255/2)), y((uchar)((v.y+1)*255/2)), z((uchar)((v.z+1)*255/2)) {}
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uchar &operator[](int i) { return v[i]; }
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uchar operator[](int i) const { return v[i]; }
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bool operator==(const bvec &v) const { return x==v.x && y==v.y && z==v.z; }
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bool operator!=(const bvec &v) const { return x!=v.x || y!=v.y || z!=v.z; }
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bool iszero() const { return x==0 && y==0 && z==0; }
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vec tovec() const { return vec(x*(2.0f/255.0f)-1.0f, y*(2.0f/255.0f)-1.0f, z*(2.0f/255.0f)-1.0f); }
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};
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struct glmatrixf
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{
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float v[16];
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float operator[](int i) const { return v[i]; }
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float &operator[](int i) { return v[i]; }
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#define ROTVEC(A, B) \
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{ \
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float a = A, b = B; \
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A = a*c + b*s; \
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B = b*c - a*s; \
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}
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void rotate_around_x(float angle)
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{
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float c = cosf(angle), s = sinf(angle);
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ROTVEC(v[4], v[8]);
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ROTVEC(v[5], v[9]);
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ROTVEC(v[6], v[10]);
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}
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void rotate_around_y(float angle)
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{
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float c = cosf(angle), s = sinf(angle);
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ROTVEC(v[8], v[0]);
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ROTVEC(v[9], v[1]);
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ROTVEC(v[10], v[2]);
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}
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void rotate_around_z(float angle)
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{
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float c = cosf(angle), s = sinf(angle);
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ROTVEC(v[0], v[4]);
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ROTVEC(v[1], v[5]);
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ROTVEC(v[2], v[6]);
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}
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#undef ROTVEC
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#define MULMAT(row, col) \
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v[col + row] = x[row]*y[col] + x[row + 4]*y[col + 1] + x[row + 8]*y[col + 2] + x[row + 12]*y[col + 3];
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template<class XT, class YT>
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void mul(const XT x[16], const YT y[16])
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{
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MULMAT(0, 0); MULMAT(1, 0); MULMAT(2, 0); MULMAT(3, 0);
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MULMAT(0, 4); MULMAT(1, 4); MULMAT(2, 4); MULMAT(3, 4);
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MULMAT(0, 8); MULMAT(1, 8); MULMAT(2, 8); MULMAT(3, 8);
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MULMAT(0, 12); MULMAT(1, 12); MULMAT(2, 12); MULMAT(3, 12);
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}
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#undef MULMAT
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void mul(const glmatrixf &x, const glmatrixf &y)
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{
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mul(x.v, y.v);
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}
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void identity()
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{
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static const float m[16] =
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{
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1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1
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};
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memcpy(v, m, sizeof(v));
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}
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void translate(float x, float y, float z)
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{
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v[12] += x;
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v[13] += y;
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v[14] += z;
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}
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void translate(const vec &o)
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{
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translate(o.x, o.y, o.z);
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}
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void scale(float x, float y, float z)
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{
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v[0] *= x; v[1] *= x; v[2] *= x; v[3] *= x;
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v[4] *= y; v[5] *= y; v[6] *= y; v[7] *= y;
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v[8] *= z; v[9] *= z; v[10] *= z; v[11] *= z;
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}
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void projective()
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{
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loopi(2) loopj(4) v[i + j*4] = 0.5f*(v[i + j*4] + v[3 + j*4]);
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}
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void invertnormal(vec &dir) const
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{
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vec n(dir);
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dir.x = n.x*v[0] + n.y*v[1] + n.z*v[2];
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dir.y = n.x*v[4] + n.y*v[5] + n.z*v[6];
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dir.z = n.x*v[8] + n.y*v[9] + n.z*v[10];
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}
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void invertvertex(vec &pos) const
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{
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vec p(pos);
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p.x -= v[12];
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p.y -= v[13];
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p.z -= v[14];
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pos.x = p.x*v[0] + p.y*v[1] + p.z*v[2];
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pos.y = p.x*v[4] + p.y*v[5] + p.z*v[6];
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pos.z = p.x*v[8] + p.y*v[9] + p.z*v[10];
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}
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float transformx(const vec &p) const
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{
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return p.x*v[0] + p.y*v[4] + p.z*v[8] + v[12];
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}
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float transformy(const vec &p) const
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{
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return p.x*v[1] + p.y*v[5] + p.z*v[9] + v[13];
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}
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float transformz(const vec &p) const
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{
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return p.x*v[2] + p.y*v[6] + p.z*v[10] + v[14];
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}
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float transformw(const vec &p) const
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{
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return p.x*v[3] + p.y*v[7] + p.z*v[11] + v[15];
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}
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void transform(const vec &in, vec4 &out) const
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{
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out.x = transformx(in);
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out.y = transformy(in);
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out.z = transformz(in);
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out.w = transformw(in);
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}
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vec gettranslation() const
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{
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return vec(v[12], v[13], v[14]);
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}
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float determinant() const;
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void adjoint(const glmatrixf &m);
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bool invert(const glmatrixf &m, float mindet = 1.0e-10f);
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};
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