699 lines
11 KiB
C++
699 lines
11 KiB
C++
#pragma once
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#include <emmintrin.h>
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#include <immintrin.h>
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#include <xmmintrin.h>
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#include <stdint.h>
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#include <assert.h>
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//clamp
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constexpr inline float clamp(float min, float a, float max) {
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float result = a;
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if (a < min)
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result = min;
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if (a > max)
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result = max;
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return result;
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}
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//clamp für 0-1 Bereich (Grafik)
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constexpr inline float clamp01(float a) {
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return clamp(0, a, 1);
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}
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//wurzelberechnung
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inline float square_root(float a) {
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return _mm_cvtss_f32(_mm_sqrt_ss(_mm_set_ss(a)));
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}
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inline float reciprocal_square_root(float a) {
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return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(a)));
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}
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constexpr inline float min(float a, float b) {
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return a < b ? a : b;
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}
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constexpr inline float max(float a, float b) {
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return a > b ? a : b;
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}
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constexpr inline double min(double a, double b) {
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return a < b ? a : b;
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}
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constexpr inline double max(double a, double b) {
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return a > b ? a : b;
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}
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constexpr inline int64_t min(int64_t a, int64_t b) {
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return a < b ? a : b;
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}
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template<typename T>
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constexpr inline T min(T a, T b) {
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return a < b ? a : b;
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}
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constexpr float lerp(float a, float t, float b) {
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return (1.0f - t) * a + t * b;
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}
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//-----------------------------------------------
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//Vektorberechnung 2-dim
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union V2 {
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struct {
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float x;
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float y;
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};
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struct {
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float u;
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float v;
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};
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struct {
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float width;
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float height;
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};
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struct {
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float E[2];
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};
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float operator [](size_t index) {
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assert(index < 2);
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return E[index];
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}
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};
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//Negation von 2-dim Vektor
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inline V2 operator -(V2 a) {
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return {
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-a.x,
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-a.y
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};
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}
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//Addition 2er 2-dim Vektoren
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inline V2 operator +(V2 a, V2 b) {
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return {
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a.x + b.x,
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a.y + b.y
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};
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}
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//Subtraktion 2er 2-dim Vektoren
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inline V2 operator -(V2 a, V2 b) {
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return {
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a.x - b.x,
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a.y - b.y
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};
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}
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//Skalarmultiplikation -> erst Skalar, dann Vektor
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inline V2 operator *(float a, V2 b) {
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return {
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a * b.x,
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a * b.y
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};
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}
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//Skalarmultiplikation -> erst Vektor, dann Skalar
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inline V2 operator *(V2 a, float b) {
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return {
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a.x * b,
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a.y * b
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};
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}
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//Division mit nem Skalar Oo -> Skalar geteilt durch Vektor
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inline V2 operator /(float a, V2 b) {
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return {
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a / b.x,
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a / b.y
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};
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}
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//Division mit nem Skalar Oo -> Vektor geteilt durch Skalar
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inline V2 operator /(V2 a, float b) {
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return {
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a.x / b,
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a.y / b
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};
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}
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//Skalarprodukt
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inline float dot(V2 a, V2 b) {
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return a.x * b.x + a.y * b.y;
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}
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//Hadamard-Produkt
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inline V2 hadamard(V2 a, V2 b) {
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return {
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a.x * b.x,
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a.y * b.y
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};
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}
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//Betrag des Vektors quadrieren
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inline float length_squared(V2 a) {
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return dot(a, a);
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}
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//Betrag eines Vektors
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inline float length(V2 a) {
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return square_root(length_squared(a));
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}
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//Reziproke der Länge
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inline float reciprocal_length(V2 a) {
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return reciprocal_square_root(length_squared(a));
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}
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//Einheitsvektor
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inline V2 normalize(V2 a) {
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return a * reciprocal_length(a);
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}
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//Vektor der 90°
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inline V2 perp(V2 a) {
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return {
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-a.y,
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a.x
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};
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}
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//clamp für 2-dim Vektor
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inline V2 clamp01(V2 a) {
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return {
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clamp01(a.x),
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clamp01(a.y)
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};
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}
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inline V2 min(V2 a, V2 b) {
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return {
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min(a.x, b.x),
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min(a.y, b.y),
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};
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}
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inline V2 max(V2 a, V2 b) {
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return {
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max(a.x, b.x),
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max(a.y, b.y),
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};
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}
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inline float min(V2 a) {
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return min(a.x, a.y);
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}
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inline float max(V2 a) {
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return max(a.x, a.y);
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}
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//-----------------------------------------------
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//Vektorberechnung 3-dim
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union V3 {
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struct {
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float x;
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float y;
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float z;
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};
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//farbvektor
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struct {
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float r;
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float g;
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float b;
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};
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//texturvektor
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struct {
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float u;
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float v;
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float s;
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};
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//von V3 zu V2 ohne z
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struct {
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V2 xy;
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float _z;
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};
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//von V3 zu V2 ohne x
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struct {
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float _x;
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V2 yz;
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};
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struct {
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float E[3];
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};
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float operator [](size_t index) {
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assert(index < 3);
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return E[index];
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}
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};
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//Negation von 2-dim Vektor
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inline V3 operator -(V3 a) {
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return {
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-a.x,
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-a.y,
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-a.z
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};
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}
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//Addition 2er 2-dim Vektoren
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inline V3 operator +(V3 a, V3 b) {
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return {
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a.x + b.x,
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a.y + b.y,
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a.z + b.z
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};
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}
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//Subtraktion 2er 2-dim Vektoren
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inline V3 operator -(V3 a, V3 b) {
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return {
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a.x - b.x,
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a.y - b.y,
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a.z - b.z
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};
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}
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//Skalarmultiplikation -> erst Skalar, dann Vektor
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inline V3 operator *(float a, V3 b) {
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return {
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a * b.x,
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a * b.y,
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a * b.z
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};
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}
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//Skalarmultiplikation -> erst Vektor, dann Skalar
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inline V3 operator *(V3 a, float b) {
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return {
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a.x * b,
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a.y * b,
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a.z * b
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};
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}
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//Division mit nem Skalar Oo -> Skalar geteilt durch Vektor
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inline V3 operator /(float a, V3 b) {
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return {
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a / b.x,
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a / b.y,
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a / b.z
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};
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}
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//Division mit nem Skalar Oo -> Vektor geteilt durch Skalar
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inline V3 operator /(V3 a, float b) {
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return {
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a.x / b,
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a.y / b,
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a.z / b
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};
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}
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//Skalarprodukt
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inline float dot(V3 a, V3 b) {
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return a.x * b.x + a.y * b.y + a.z * b.z;
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}
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//Hadamard-Produkt
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inline V3 hadamard(V3 a, V3 b) {
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return {
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a.x * b.x,
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a.y * b.y,
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a.z * b.z
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};
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}
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//Kreuzprodukt
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inline V3 cross(V3 a, V3 b) {
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return {
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a.y * b.z - a.z * b.y,
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a.z * b.x - a.x * b.z,
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a.x * b.y - a.y * b.x
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};
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}
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//Betrag des Vektors quadrieren
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inline float length_squared(V3 a) {
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return dot(a, a);
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}
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//Betrag eines Vektors
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inline float length(V3 a) {
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return square_root(length_squared(a));
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}
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//Reziproke der Länge
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inline float reciprocal_length(V3 a) {
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return reciprocal_square_root(length_squared(a));
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}
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//Einheitsvektor
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inline V3 normalize(V3 a) {
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return a * reciprocal_length(a);
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}
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union V4 {
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struct {
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float x;
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float y;
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float z;
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float w;
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};
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//farbvektor
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struct {
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float r;
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float g;
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float b;
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float a;
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};
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//texturvektor
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struct {
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float u;
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float v;
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float s;
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float t;
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};
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//von V3 zu V2 ohne z
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struct {
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V2 xy;
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V2 zw;
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};
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//von V3 zu V2 ohne x
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struct {
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float _x;
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V2 yz;
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float _w;
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};
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struct {
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float E[4];
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};
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V4(V2 a, V2 b) { xy = a; zw = b; }
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V4(float a, float b, float c, float d) { x = a; y = b; z = c; w = d; }
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V4(float a, float b, float c) { x = a; y = b; z = c; w = 1; }
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V4() {}
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float operator [](size_t index) {
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assert(index < 4);
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return E[index];
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}
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};
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//-----------------------------------------------
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//2x2 Matrix
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//M2x2 m;
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//m.E[0][1]
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//m.V[1]
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//m[1][0]
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union M2x2 {
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struct {
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float x1; float x2;
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float y1; float y2;
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};
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struct {
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float E[2][2];
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};
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struct {
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V2 V[2];
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};
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V2 &operator [](size_t index) {
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assert(index < 2);
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return V[index];
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}
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};
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//Matrix negieren
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inline M2x2 operator -(M2x2 a){
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return {
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-a[0][0], -a[0][1],
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-a[1][0], -a[1][1]
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};
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}
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//Matrix Addition
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inline M2x2 operator +(M2x2 a, M2x2 b) {
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return {
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a[0][0] + b[0][0], a[0][1] + b[0][1],
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a[1][0] + b[1][0], a[1][1] + b[1][1]
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};
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}
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//Matrix Subtraktion
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inline M2x2 operator -(M2x2 a, M2x2 b) {
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return {
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a[0][0] - b[0][0], a[0][1] - b[0][1],
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a[1][0] - b[1][0], a[1][1] - b[1][1]
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};
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}
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//Matrix Skalarmultiplikation
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inline M2x2 operator *(M2x2 a, float b) {
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return {
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a[0][0] * b, a[0][1] * b,
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a[1][0] * b, a[1][1] * b
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};
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}
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//Matrix Skalarmultiplikation
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inline M2x2 operator *(float a, M2x2 b) {
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return {
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a * b[0][0], a * b[0][1],
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a * b[1][0], a * b[1][1]
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};
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}
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//Matrix Multiplikation
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inline M2x2 operator *(M2x2 a, M2x2 b) {
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return {
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a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1],
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a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]
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};
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}
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//Matrix * Vektor
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inline V2 operator *(M2x2 a, V2 b) {
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return {
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a[0][0] * b[0] + a[0][1] * b[1],
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a[1][0] * b[0] + a[1][1] * b[1],
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};
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}
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//Matrix Transponieren
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inline M2x2 transpose(M2x2 a) {
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return {
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a[0][0], a[1][0],
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a[0][1], a[1][1]
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};
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}
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//Einheitsmatrix (oder Identitätsmatrix)
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constexpr inline M2x2 identityM2x2() {
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return {
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1.0f, 0.0f,
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0.0f, 1.0f
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};
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}
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//-----------------------------------------------
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//3x3 Matrix
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union M3x3 {
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struct {
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float x1; float x2; float x3;
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float y1; float y2; float y3;
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float z1; float z2; float z3;
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};
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struct {
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float E[3][3];
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};
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struct {
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V3 V[3];
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};
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V3& operator [](size_t index) {
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assert(index < 3);
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return V[index];
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}
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};
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//Matrix negieren
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inline M3x3 operator -(M3x3 a) {
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return {
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-a[0][0], -a[0][1], -a[0][1],
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-a[1][0], -a[1][1], -a[1][2],
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-a[2][0], -a[2][1], -a[2][2]
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};
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}
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//Matrix Addition
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inline M3x3 operator +(M3x3 a, M3x3 b) {
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return {
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a[0][0] + b[0][0], a[0][1] + b[0][1], a[0][2] + b[0][2],
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a[1][0] + b[1][0], a[1][1] + b[1][1], a[1][2] + b[1][2],
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a[2][0] + b[2][0], a[2][1] + b[2][1], a[2][2] + b[2][2]
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};
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}
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//Matrix Subtraktion
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inline M3x3 operator -(M3x3 a, M3x3 b) {
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return {
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a[0][0] - b[0][0], a[0][1] - b[0][1], a[0][2] - b[0][2],
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a[1][0] - b[1][0], a[1][1] - b[1][1], a[1][2] - b[1][2],
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a[2][0] - b[2][0], a[2][1] - b[2][1], a[2][2] - b[2][2]
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};
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}
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//Matrix Skalarmultiplikation
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inline M3x3 operator *(M3x3 a, float b) {
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return {
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a[0][0] * b, a[0][1] * b, a[0][2] * b,
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a[1][0] * b, a[1][1] * b, a[1][2] * b,
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a[2][0] * b, a[2][1] * b, a[2][2] * b
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};
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}
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//Matrix Skalarmultiplikation
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inline M3x3 operator *(float a, M3x3 b) {
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return {
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a * b[0][0], a * b[0][1], a * b[0][2],
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a * b[1][0], a * b[1][1], a * b[1][2],
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a * b[2][0], a * b[2][1], a * b[2][2]
|
|
};
|
|
}
|
|
|
|
//Matrix Multiplikation
|
|
inline M3x3 operator *(M3x3 a, M3x3 b) {
|
|
return {
|
|
a[0][0] * b[0][0] + a[0][1] * b[1][0] + a[0][2] * b[2][0], a[0][0] * b[0][1] + a[0][1] * b[1][1] + a[0][2] * b[2][1], a[0][0] * b[0][2] + a[0][1] * b[1][2] + a[0][2] * b[2][2],
|
|
a[1][0] * b[0][0] + a[1][1] * b[1][0] + a[1][2] * b[2][0], a[1][0] * b[0][1] + a[1][1] * b[1][1] + a[1][2] * b[2][1], a[1][0] * b[0][2] + a[1][1] * b[1][2] + a[0][2] * b[2][2],
|
|
a[2][0] * b[0][0] + a[2][1] * b[1][0] + a[2][2] * b[2][0], a[2][0] * b[0][1] + a[2][1] * b[1][1] + a[2][2] * b[2][1], a[2][0] * b[0][2] + a[2][1] * b[1][2] + a[0][2] * b[2][2]
|
|
};
|
|
}
|
|
|
|
//Matrix * V2
|
|
inline V2 operator *(M3x3 a, V2 b) {
|
|
return {
|
|
b.x * a[0][0] + b.y * a[0][1] + 1.0f * a[0][2],
|
|
b.x * a[1][0] + b.y * a[1][1] + 1.0f * a[1][2],
|
|
};
|
|
}
|
|
|
|
//Matrix * V3
|
|
inline V3 operator *(M3x3 a, V3 b) {
|
|
return {
|
|
b.x * a[0][0] + b.y * a[0][1] + b.z * a[0][2],
|
|
b.x * a[1][0] + b.y * a[1][1] + b.z * a[1][2],
|
|
b.x * a[2][0] + b.y * a[2][1] + b.z * a[2][2]
|
|
};
|
|
}
|
|
|
|
|
|
//Matrix transponieren
|
|
inline M3x3 transpose(M3x3 a) {
|
|
return {
|
|
a[0][0], a[1][0], a[2][0],
|
|
a[0][1], a[1][1], a[2][1],
|
|
a[0][2], a[1][2], a[2][2]
|
|
};
|
|
}
|
|
|
|
//Einheitsmatrix (oder Identitätsmatrix)
|
|
inline M3x3 identityM3x3() {
|
|
return {
|
|
1.0f, 0.0f, 0.0f,
|
|
0.0f, 1.0f, 0.0f,
|
|
0.0f, 0.0f, 1.0f
|
|
};
|
|
}
|
|
|
|
|
|
|
|
//-----------------------------------------------
|
|
//m128i
|
|
struct m128i {
|
|
__m128i val;
|
|
};
|
|
|
|
inline __m128i operator &(m128i a, m128i b) {
|
|
return _mm_and_si128(a.val, b.val);
|
|
}
|
|
|
|
inline __m128i operator |(m128i a, m128i b) {
|
|
return _mm_or_si128(a.val, b.val);
|
|
}
|
|
|
|
inline __m128i operator >>(m128i a, int b) {
|
|
return _mm_srli_epi32(a.val, b);
|
|
}
|
|
|
|
inline __m128i operator <<(m128i a, int b) {
|
|
return _mm_slli_epi32(a.val, b);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------
|
|
//m128
|
|
struct m128 {
|
|
__m128 val;
|
|
};
|
|
|
|
inline __m128 operator +(m128 a, m128 b) {
|
|
return _mm_mul_ps(a.val, b.val);
|
|
}
|
|
|
|
inline __m128 operator *(m128 a, m128 b) {
|
|
return _mm_mul_ps(a.val, b.val);
|
|
}
|
|
|
|
inline __m128 operator *(float a, m128 b) {
|
|
return _mm_mul_ps(_mm_set1_ps(a), b.val);
|
|
}
|
|
|
|
inline __m128 square_root(__m128 a) {
|
|
return _mm_sqrt_ps(a);
|
|
}
|
|
|
|
inline __m128 operator /(m128 a, m128 b) {
|
|
return _mm_div_ps(a.val, b.val);
|
|
}
|
|
|
|
inline __m128 lerp(__m128 a, float t, float b) {
|
|
return (1.0f - t) * a + (t * b);
|
|
} |