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23
inc/hgl/math/FastTriangle.h
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23
inc/hgl/math/FastTriangle.h
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#ifndef HGL_ALGORITHM_MATH_FAST_TRIANGLE_FUNCTION_INCLUDE
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#define HGL_ALGORITHM_MATH_FAST_TRIANGLE_FUNCTION_INCLUDE
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namespace hgl
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{
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double Lsin(int angle); ///<低精度sin计算,注意传入的参数为角度而非弧度
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double Lcos(int angle); ///<低精度cos计算,注意传入的参数为角度而非弧度
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void Lsincos(int angle, double &s, double &c); ///<低精度sin+cos计算,注意传入的参数为角度而非弧度
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/**
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* 低精度atan函数
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*/
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double inline Latan(double z)
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{
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constexpr double n1 = 0.97239411f;
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constexpr double n2 = -0.19194795f;
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return (n1 + n2 * z * z) * z;
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}
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double Latan2(double y, double x); ///<低精度atan2函数
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}//namespace hgl
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#endif//HGL_ALGORITHM_MATH_FAST_TRIANGLE_FUNCTION_INCLUDE
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8
inc/hgl/math/Math.h
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8
inc/hgl/math/Math.h
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#ifndef HGL_ALGORITHM_MATH_INCLUDE
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#define HGL_ALGORITHM_MATH_INCLUDE
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#include<hgl/math/FastTriangle.h>
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#include<hgl/math/Vector.h> // Game Math and Geometry Library
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#include<hgl/math/Matrix.h>
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#endif//HGL_ALGORITHM_MATH_INCLUDE
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156
inc/hgl/math/Matrix.h
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156
inc/hgl/math/Matrix.h
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#ifndef HGL_ALGORITHM_MATH_VECTOR_MATRIX_INCLUDE
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#define HGL_ALGORITHM_MATH_VECTOR_MATRIX_INCLUDE
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#include<hgl/math/Vector.h>
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#include<hgl/TypeFunc.h>
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//注：GLM/CML(OpenGLMode)是列矩阵,计算坐标matrix*pos
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// 而MGL是行矩阵，需要反过来pos*matrix
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namespace hgl
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{
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using Matrix3f=float3x3;
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using Matrix4f=float4x4;
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struct WorldMatrix
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{
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alignas(16) Matrix4f ortho; //2D正角视图矩阵
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alignas(16) Matrix4f projection;
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// alignas(16) Matrix4f inverse_projection;
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alignas(16) Matrix4f modelview;
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alignas(16) Matrix4f mvp;
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alignas(16) Vector4f view_pos; //眼睛坐标
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};//struct WorldMatrix
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inline Matrix4f identity()
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{
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return Matrix4f::identity;
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}
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inline Matrix4f inverse(const Matrix4f &m)
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{
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return m.Inverted();
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}
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inline Matrix4f ortho( float left,
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float right,
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float bottom,
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float top,
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float znear,
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float zfar )
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{
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return Matrix4f(
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2.0f / (right - left), 0.0f, 0.0f, -(right + left) / (right - left),
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0.0f, 2.0f / (bottom - top), 0.0f, -(bottom + top) / (bottom - top),
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0.0f, 0.0f, 1.0f / (znear - zfar), znear / (znear - zfar),
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0.0f, 0.0f, 0.0f, 1.0f);
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}
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/**
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* 生成一个正角视图矩阵
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* @param width 宽
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* @param height 高
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* @param znear 近平面z值
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* @param zfar 远平台z值
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*/
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inline Matrix4f ortho(float width,float height,float znear,float zfar)
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{
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return Matrix4f(
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2.0f / width, 0.0f, 0.0f, -1,
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0.0f, 2.0f / height, 0.0f, -1,
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0.0f, 0.0f, 1.0f / (znear - zfar), znear / (znear - zfar),
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0.0f, 0.0f, 0.0f, 1.0f);
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}
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/**
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* 生成一个正角视图矩阵
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* @param width 宽
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* @param height 高
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*/
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inline Matrix4f ortho(float width,float height)
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{
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return Matrix4f(
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2.0f / width, 0.0f, 0.0f, -1,
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0.0f, 2.0f / height, 0.0f, -1,
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0.0f, 0.0f, -1.0f , 0.0f,
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0.0f, 0.0f, 0.0f, 1.0f);
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}
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/**
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* 生成一个透视矩阵
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* @param aspect_ratio 宽高比
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* @param field_of_view 视野
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* @param znear 近截面
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* @param zfar 远截面
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*/
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inline Matrix4f perspective(float field_of_view,
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float aspect_ratio,
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float znear,
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float zfar)
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{
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const float f = 1.0f / tan( hgl_ang2rad( 0.5f * field_of_view ) );
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// float scaleX, shearXy, shearXz, x;
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//float shearYx, scaleY, shearYz, y;
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//float shearZx, shearZy, scaleZ, z;
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//float shearWx, shearWy, shearWz, w;
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return Matrix4f(
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f / aspect_ratio, 0.0f, 0.0f, 0.0f,
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0.0f, -f, 0.0f, 0.0f,
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0.0f, 0.0f, zfar / (znear - zfar), (znear * zfar) / (znear - zfar),
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// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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// 某些引擎这两项会乘0.5，那是因为他们是 -1 to 1 的Z值设定，而我们是0 to 1，所以这里不用乘
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// 同理，camera的znear为接近0的正数，zfar为一个较大的正数，默认使用16/256
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0.0f, 0.0f, -1.0f, 0.0f);
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}
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inline Matrix4f translate(const Vector3f &v)
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{
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return Matrix4f::Translate(v);
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}
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inline Matrix4f translate(float x,float y,float z)
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{
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return Matrix4f::Translate(x,y,z);
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}
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inline Matrix4f scale(const Vector3f &v)
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{
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return Matrix4f::Scale(v,Vector3f::zero);
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}
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inline Matrix4f scale(float x,float y,float z)
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{
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return Matrix4f::Scale(Vector3f(x,y,z),Vector3f::zero);
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}
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inline Matrix4f scale(float s)
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{
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return Matrix4f::Scale(Vector3f(s,s,s),Vector3f::zero);
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}
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inline Matrix4f rotate(float angle,const Vector3f &axis)
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{
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return Matrix4f::RotateAxisAngle(axis.Normalized(),angle);
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}
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inline Matrix4f rotate(float angle,float x,float y,float z)
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{
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return rotate(angle,Vector3f(x,y,z));
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}
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inline Matrix4f rotate(float angle,const Vector4f &axis)
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{
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return rotate(angle,Vector3f(axis.x,axis.y,axis.z));
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}
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inline Vector3f rotate(const Vector3f &v3f,float angle,const Vector3f &axis)
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{
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Vector4f result=rotate(angle,axis)*Vector4f(v3f,1.0f);
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return result.xyz();
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}
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}//namespace hgl
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#endif//HGL_ALGORITHM_MATH_VECTOR_MATRIX_INCLUDE
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346
inc/hgl/math/Vector.h
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346
inc/hgl/math/Vector.h
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#ifndef HGL_ALGORITHM_MATH_VECTOR_INCLUDE
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#define HGL_ALGORITHM_MATH_VECTOR_INCLUDE
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#ifdef _MSC_VER
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#pragma warning(disable:4244) // double -> int 精度丢失警告
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#endif//_MSC_VER
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#include<hgl/math/FastTriangle.h>
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#include<MathGeoLib.h>
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/**
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* MathGeoLib
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* Game Math and Geometry Library
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*
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* My C++ library for 3D mathematics and geometry manipulation.
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* Jukka Jylänki
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*
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* offical web: http://clb.demon.fi/MathGeoLib/nightly/
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*
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* License:
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*
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* This library is licensed under the Apache 2 license. I am not a lawyer, but to me that
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* license means that you can use this code for any purpose, both commercial and closed source.
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* You are however restricted from claiming you wrote it yourself, and cannot hold me liable
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* for anything over this code.
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* I acknowledge that most of the non-trivial math routines are taken off a book or a
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* research paper. In all places, I have tried to be diligent to properly attribute the original
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* source. Please contact me if you feel I have misattributed something.
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*/
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namespace hgl
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{
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using Vector2f=float2;
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using Vector3f=float3;
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using Vector4f=float4;
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inline bool operator == (const Vector2f &lhs,const Vector2f &rhs)
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{
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if(lhs.x!=rhs.x)return(false);
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if(lhs.y!=rhs.y)return(false);
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return(true);
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}
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inline bool operator != (const Vector2f &lhs,const Vector2f &rhs)
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{
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if(lhs.x!=rhs.x)return(true);
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if(lhs.y!=rhs.y)return(true);
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return(false);
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}
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inline bool operator == (const Vector3f &lhs,const Vector3f &rhs)
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{
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if(lhs.x!=rhs.x)return(false);
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if(lhs.y!=rhs.y)return(false);
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if(lhs.z!=rhs.z)return(false);
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return(true);
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}
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inline bool operator != (const Vector3f &lhs,const Vector3f &rhs)
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{
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if(lhs.x!=rhs.x)return(true);
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if(lhs.y!=rhs.y)return(true);
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if(lhs.z!=rhs.z)return(true);
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return(false);
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}
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inline bool operator == (const Vector4f &lhs,const Vector4f &rhs)
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{
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if(lhs.x!=rhs.x)return(false);
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if(lhs.y!=rhs.y)return(false);
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if(lhs.z!=rhs.z)return(false);
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if(lhs.w!=rhs.w)return(false);
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return(true);
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}
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inline bool operator != (const Vector4f &lhs,const Vector4f &rhs)
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{
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if(lhs.x!=rhs.x)return(true);
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if(lhs.y!=rhs.y)return(true);
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if(lhs.z!=rhs.z)return(true);
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if(lhs.w!=rhs.w)return(true);
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return(false);
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}
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inline void vec3to2(Vector2f &dst,const Vector3f &src)
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{
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dst.x=src.x;
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dst.y=src.y;
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}
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inline Vector2f vec3to2(const Vector3f &src)
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{
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return Vector2f(src.x,src.y);
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}
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inline void vec2to3(Vector3f &dst,const Vector2f &src,const float z)
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{
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dst.x=src.x;
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dst.y=src.y;
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dst.z=z;
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}
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inline Vector3f vec2to3(const Vector2f &src,const float z)
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{
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return Vector3f(src.x,src.y,z);
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}
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template<typename T>
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inline T normalized(const T &v)
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{
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return v.Normalized();
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}
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template<typename T>
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inline void normalize(T &v)
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{
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v.Normalize();
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}
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template<typename T>
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inline T cross(const T &v1,const T &v2)
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{
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return v1.Cross(v2);
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}
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template<typename T>
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inline float dot(const T &v1,const T &v2)
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{
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return v1.Dot(v2);
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}
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inline float ray_angle_cos(const Ray &ray,const vec &pos)
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{
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return ray.dir.Dot((pos-ray.pos).Normalized());
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}
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inline float length_squared(const Vector2f &v)
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{
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return (v.x*v.x) + (v.y*v.y);
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}
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inline float length_squared_2d(const Vector3f &v)
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{
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return (v.x*v.x) + (v.y*v.y);
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}
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inline float length_squared(const Vector3f &v)
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{
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return (v.x*v.x) + (v.y*v.y) + (v.z*v.z);
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}
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inline float length_squared(const Vector4f &v)
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{
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return (v.x*v.x) + (v.y*v.y) + (v.z*v.z);
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}
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template<typename T>
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inline float length(const T &v)
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{
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return sqrt(length_squared(v));
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}
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inline float length_2d(const Vector3f &v)
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{
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return sqrt(length_squared_2d(v));
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}
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template<typename T1, typename T2>
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inline float length_squared(const T1 &v1, const T2 &v2)
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{
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const float x = (v1.x - v2.x);
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const float y = (v1.y - v2.y);
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return x*x + y*y;
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}
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template<typename T1, typename T2>
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inline float length(const T1 &v1, const T2 &v2)
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{
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return sqrt(length_squared(v1, v2));
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}
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inline float length_squared(const Vector3f &v1, const Vector3f &v2)
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{
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const float x = (v1.x - v2.x);
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const float y = (v1.y - v2.y);
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const float z = (v1.z - v2.z);
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return x*x + y*y + z*z;
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}
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template<typename T1, typename T2>
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inline float length_squared_2d(const T1 &v1, const T2 &v2)
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{
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const float x = (v1.x - v2.x);
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const float y = (v1.y - v2.y);
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return x*x + y*y;
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}
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inline float length(const Vector3f &v1, const Vector3f &v2)
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||||
{
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return sqrt(length_squared(v1, v2));
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}
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template<typename T1, typename T2>
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inline float length_2d(const T1 &v1, const T2 &v2)
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{
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return sqrt(length_squared_2d(v1, v2));
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}
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inline Vector2f to(const Vector2f &start, const Vector2f &end, float pos)
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{
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return Vector2f(start.x + (end.x - start.x)*pos,
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start.y + (end.y - start.y)*pos);
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}
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inline Vector3f to(const Vector3f &start, const Vector3f &end, float pos)
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{
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return Vector3f(start.x + (end.x - start.x)*pos,
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start.y + (end.y - start.y)*pos,
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start.z + (end.z - start.z)*pos);
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}
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template<typename T>
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inline void to_2d(T &result, const T &start, const T &end, float pos)
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{
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result.x = start.x + (end.x - start.x)*pos;
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result.y = start.y + (end.y - start.y)*pos;
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}
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inline float ray_angle_cos(const Vector3f &ray_dir, const Vector3f &ray_pos, const Vector3f &pos)
|
||||
{
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return dot(ray_dir, normalized(pos - ray_pos));
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||||
}
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||||
|
||||
/**
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||||
* 做一个2D旋转计算
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||||
* @param result 结果
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||||
* @param source 原始点坐标
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* @param center 圆心坐标
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* @param ang 旋转角度
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||||
*/
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template<typename T1, typename T2, typename T3>
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inline void rotate2d(T1 &result, const T2 &source, const T3 ¢er, const double ang)
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||||
{
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double as, ac;
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// double nx,ny;
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||||
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||||
// as=sin(ang*(HGL_PI/180.0f));
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// ac=cos(ang*(HGL_PI/180.0f));
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//sincos(ang*(HGL_PI/180.0f),&as,&ac); //在80x87指令上，sin/cos是一个指令同时得出sin和cos，所以可以这样做
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Lsincos(ang, as, ac); //低精度sin/cos计算
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||||
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result.x = center.x + ((source.x - center.x)*ac - (source.y - center.y)*as);
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||||
result.y = center.y + ((source.x - center.x)*as + (source.y - center.y)*ac);
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||||
}
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||||
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||||
template<typename T> union vec2
|
||||
{
|
||||
struct { T x,y; };
|
||||
struct { T r,g; };
|
||||
struct { T u,v; };
|
||||
T data[2];
|
||||
|
||||
public:
|
||||
|
||||
vec2(){x=y=0;}
|
||||
vec2(T v1,T v2):x(v1),y(v2){}
|
||||
vec2(const vec2 &v2)
|
||||
{
|
||||
x=v2.x;
|
||||
y=v2.y;
|
||||
}
|
||||
|
||||
vec2(const Vector2f &v2f)
|
||||
{
|
||||
x=v2f.x;
|
||||
y=v2f.y;
|
||||
}
|
||||
|
||||
operator const Vector2f()const{return Vector2f(x,y);}
|
||||
};
|
||||
|
||||
template<typename T> union vec3
|
||||
{
|
||||
struct { T x,y,z; };
|
||||
struct { T r,g,b; };
|
||||
struct { T u,v,w; };
|
||||
T data[3];
|
||||
|
||||
public:
|
||||
|
||||
vec3(){x=y=z=0;}
|
||||
vec3(T v1,T v2,T v3):x(v1),y(v2),z(v3){}
|
||||
vec3(const vec3 &v3)
|
||||
{
|
||||
x=v3.x;
|
||||
y=v3.y;
|
||||
z=v3.z;
|
||||
}
|
||||
|
||||
vec3(const Vector3f &v3f)
|
||||
{
|
||||
x=v3f.x;
|
||||
y=v3f.y;
|
||||
z=v3f.z;
|
||||
|
||||
return *this;
|
||||
}
|
||||
|
||||
operator const Vector3f()const{return Vector3f(x,y,z);}
|
||||
};
|
||||
|
||||
template<typename T> union vec4
|
||||
{
|
||||
struct { T x,y,z,w; };
|
||||
struct { T r,g,b,a; };
|
||||
T data[4];
|
||||
|
||||
public:
|
||||
|
||||
vec4(){x=y=z=w=0;}
|
||||
vec4(T v1,T v2,T v3,T v4):x(v1),y(v2),z(v3),w(v4){}
|
||||
vec4(const vec4 &v4)
|
||||
{
|
||||
x=v4.x;
|
||||
y=v4.y;
|
||||
z=v4.z;
|
||||
w=v4.w;
|
||||
}
|
||||
|
||||
vec4(const Vector4f &v4f)
|
||||
{
|
||||
x=v4f.x;
|
||||
y=v4f.y;
|
||||
z=v4f.z;
|
||||
w=v4f.w;
|
||||
|
||||
return *this;
|
||||
}
|
||||
|
||||
operator const Vector4f()const{return Vector4f(x,y,z,w);}
|
||||
};
|
||||
}//namespace hgl
|
||||
#endif//HGL_ALGORITHM_MATH_VECTOR_INCLUDE
|
||||
Reference in New Issue
Block a user