step2：model + view matrix
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@ -58,16 +58,24 @@
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@ -77,7 +85,8 @@
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<ConformanceMode>true</ConformanceMode>
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<LanguageStandard>stdcpp20</LanguageStandard>
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@ -95,7 +104,8 @@
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@ -111,7 +121,8 @@
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@ -129,7 +140,8 @@
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<ConformanceMode>true</ConformanceMode>
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<Link>
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<SubSystem>Console</SubSystem>
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@ -146,6 +158,7 @@
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<ClCompile Include="main.cpp" />
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<ClCompile Include="Rasterizer\Rasterizer.cpp" />
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<ClCompile Include="Rasterizer\TriangleRasterizer.cpp" />
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<ClCompile Include="Scene\Camera.cpp" />
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<ClCompile Include="Shading\BlinnPhongShader.cpp" />
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</ItemGroup>
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<ItemGroup>
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@ -1,7 +1,96 @@
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#pragma once
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#include "Matrix4x4.h"
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#include "Vector3.h"
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#include <cmath>
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namespace Math
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{
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class MathUtil
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{};
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static class MathUtil
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{
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public:
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static Matrix4x4 get_translate_matrix(const float x, const float y, const float z) { return get_translate_matrix(Vector3(x, y, z)); }
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static Matrix4x4 get_translate_matrix(const Vector3& translation)
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{
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return Matrix4x4(
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1, 0, 0, translation.x,
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0, 1, 0, translation.y,
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0, 0, 1, translation.z,
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0, 0, 0, 0
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);
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}
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static Matrix4x4 get_scale_matrix(const float x, const float y, const float z) { return get_scale_matrix(Vector3(x, y, z)); }
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static Matrix4x4 get_scale_matrix(const Vector3& scale)
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{
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return Matrix4x4(
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scale.x, 0, 0, 0,
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0, scale.y, 0, 0,
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0, 0, scale.z, 0,
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0, 0, 0, 1
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);
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}
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static Matrix4x4 get_rotation_matrix_x(const float radians)
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{
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const float cosValue = std::cos(radians);
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const float sinValue = std::sin(radians);
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return Matrix4x4(
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1, 0, 0, 0,
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0, cosValue, -sinValue, 0,
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0, sinValue, cosValue, 0,
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0, 0, 0, 1
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);
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}
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static Matrix4x4 get_rotation_matrix_y(const float radians)
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{
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const float cosValue = std::cos(radians);
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const float sinValue = std::sin(radians);
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return Matrix4x4(
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cosValue, sinValue, 0, 0,
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0, 1, 0, 0,
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-sinValue, cosValue, 0, 0,
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0, 0, 0, 1
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);
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}
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static Matrix4x4 get_rotation_matrix_z(const float radians)
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{
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const float cosValue = std::cos(radians);
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const float sinValue = std::sin(radians);
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return Matrix4x4(
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cosValue, -sinValue, 0, 0,
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sinValue, cosValue, 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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}
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static Matrix4x4 get_rotation_matrix(const Vector3& rotation)
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{
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return get_rotation_matrix_z(rotation.z) * get_rotation_matrix_y(rotation.y) * get_rotation_matrix_x(rotation.x);
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}
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static Matrix4x4 get_rodrigues_rotation_matrix(const Vector3& axis, const float radians)
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{
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const float cosValue = std::cos(radians);
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const float sinValue = std::sin(radians);
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const float oneMinusCos = 1.0f - cosValue;
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const float powX = axis.x * axis.x;
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const float powY = axis.y * axis.y;
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const float powZ = axis.z * axis.z;
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return Matrix4x4(
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1 + 0 + oneMinusCos * (-powZ - powY), 0 + sinValue * (-axis.z) + oneMinusCos * axis.x * axis.y, 0 + sinValue * axis.z + oneMinusCos * axis.x * axis.z, 0,
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0 + sinValue * axis.z + oneMinusCos * axis.x * axis.y, 1 + 0 + oneMinusCos * (-powZ - powX), 0 + sinValue * (-axis.x) + oneMinusCos * axis.y * axis.z, 0,
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0 + sinValue * (-axis.y) + oneMinusCos * axis.x * axis.z, 0 + sinValue * axis.x + oneMinusCos * axis.y * axis.z, 1 + 0 + oneMinusCos * (-powY - powX), 0,
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0, 0, 0, 1
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);
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}
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};
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}
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@ -1,7 +1,177 @@
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#pragma once
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#include <cmath>
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#include "Vector3.h"
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#include "Vector4.h"
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namespace Math
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{
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class Matrix4x4
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{};
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{
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public:
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// 约定：
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// - 图形转换使用列向量语义
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// - 图形变换按列向量语义做，写法是 M * v
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// - 元素访问是 matrix[row][col]
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// - data() 暴露的是 row-major 连续内存
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// - 平移放在最后一列
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Matrix4x4()
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{
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*this = Identity();
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}
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Matrix4x4(
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float m00, float m01, float m02, float m03,
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float m10, float m11, float m12, float m13,
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float m20, float m21, float m22, float m23,
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float m30, float m31, float m32, float m33)
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{
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values[0][0] = m00; values[0][1] = m01; values[0][2] = m02; values[0][3] = m03;
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values[1][0] = m10; values[1][1] = m11; values[1][2] = m12; values[1][3] = m13;
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values[2][0] = m20; values[2][1] = m21; values[2][2] = m22; values[2][3] = m23;
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values[3][0] = m30; values[3][1] = m31; values[3][2] = m32; values[3][3] = m33;
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}
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static Matrix4x4 Zero()
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{
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return Matrix4x4(
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0.0f, 0.0f, 0.0f, 0.0f,
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0.0f, 0.0f, 0.0f, 0.0f,
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0.0f, 0.0f, 0.0f, 0.0f,
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0.0f, 0.0f, 0.0f, 0.0f
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);
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}
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static Matrix4x4 Identity()
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{
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return Matrix4x4(
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1.0f, 0.0f, 0.0f, 0.0f,
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0.0f, 1.0f, 0.0f, 0.0f,
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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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float* operator[](size_t row)
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{
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return values[row];
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}
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const float* operator[](size_t row) const
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{
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return values[row];
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}
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float* data()
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{
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return &values[0][0];
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}
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const float* data() const
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{
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return &values[0][0];
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}
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Matrix4x4 operator+ (const Matrix4x4& other) const
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{
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Matrix4x4 result = Zero();
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for (size_t row = 0; row < 4; ++row)
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{
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for (size_t col = 0; col < 4; ++col)
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{
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result[row][col] = values[row][col] + other[row][col];
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}
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}
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return result;
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}
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Matrix4x4 operator- (const Matrix4x4& other) const
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{
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Matrix4x4 result = Zero();
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for (size_t row = 0; row < 4; ++row)
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{
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for (size_t col = 0; col < 4; ++col)
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{
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result[row][col] = values[row][col] - other[row][col];
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}
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}
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return result;
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}
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Matrix4x4 operator* (float scalar) const
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{
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Matrix4x4 result = Zero();
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for (size_t row = 0; row < 4; ++row)
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{
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for (size_t col = 0; col < 4; ++col)
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{
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result[row][col] = values[row][col] * scalar;
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}
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}
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return result;
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}
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// 结果为 this x other（调用方 乘以 参数）。
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Matrix4x4 operator* (const Matrix4x4& other) const
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{
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Matrix4x4 result = Zero();
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for (size_t row = 0; row < 4; ++row)
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{
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for (size_t col = 0; col < 4; ++col)
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{
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for (size_t k = 0; k < 4; ++k)
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{
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result[row][col] += values[row][k] * other[k][col];
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}
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}
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}
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return result;
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}
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// 结果为 this x other（调用方 乘以 参数）。
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Vector4 operator* (const Vector4& vector) const
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{
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return Vector4(
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values[0][0] * vector.x + values[0][1] * vector.y + values[0][2] * vector.z + values[0][3] * vector.w,
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values[1][0] * vector.x + values[1][1] * vector.y + values[1][2] * vector.z + values[1][3] * vector.w,
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values[2][0] * vector.x + values[2][1] * vector.y + values[2][2] * vector.z + values[2][3] * vector.w,
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values[3][0] * vector.x + values[3][1] * vector.y + values[3][2] * vector.z + values[3][3] * vector.w
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);
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}
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Vector4 TransformPoint(const Vector3& point) const
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{
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return *this * Vector4::Point(point);
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}
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Vector4 TransformDirection(const Vector3& direction) const
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{
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return *this * Vector4::Direction(direction);
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}
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Matrix4x4 Transposed() const
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{
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Matrix4x4 result = Zero();
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for (size_t row = 0; row < 4; ++row)
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{
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for (size_t col = 0; col < 4; ++col)
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{
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result[row][col] = values[col][row];
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}
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}
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return result;
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}
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private:
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float values[4][4] = {};
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};
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inline Matrix4x4 operator* (float scalar, const Matrix4x4& matrix)
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{
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return matrix * scalar;
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}
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}
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@ -12,9 +12,74 @@ namespace Math
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Vector3() : x(0), y(0), z(0) {}
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Vector3(float x, float y, float z) : x(x), y(y), z(z) {}
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float sqrMagnitude() const
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{
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return x * x + y * y + z * z;
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}
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float magnitude() const
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{
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return std::sqrt(x * x + y * y + z * z);
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return std::sqrt(sqrMagnitude());
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}
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Vector3 normalized() const
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{
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const float length = magnitude();
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if (length <= 0.0f)
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{
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return Vector3();
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}
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return *this / length;
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}
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float dot(const Vector3& other) const
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{
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return x * other.x + y * other.y + z * other.z;
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}
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// Returns this x other.
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// Order matters:
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// - a.cross(b) == -(b.cross(a))
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// - the result follows the right-hand rule
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// - cross product is not associative
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Vector3 cross(const Vector3& other) const
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{
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return Vector3(
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y * other.z - z * other.y,
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z * other.x - x * other.z,
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x * other.y - y * other.x
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);
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}
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Vector3 operator+ (const Vector3& other) const
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{
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return Vector3(x + other.x, y + other.y, z + other.z);
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}
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Vector3 operator- (const Vector3& other) const
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{
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return Vector3(x - other.x, y - other.y, z - other.z);
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}
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Vector3 operator- () const
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{
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return Vector3(-x, -y, -z);
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}
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Vector3 operator* (float scalar) const
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{
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return Vector3(x * scalar, y * scalar, z * scalar);
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}
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Vector3 operator/ (float scalar) const
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{
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return Vector3(x / scalar, y / scalar, z / scalar);
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}
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};
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inline Vector3 operator* (float scalar, const Vector3& vector)
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{
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return vector * scalar;
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}
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}
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@ -1,7 +1,83 @@
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#pragma once
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#include <cmath>
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#include "Vector3.h"
|
||||
|
||||
namespace Math
|
||||
{
|
||||
class Vector4
|
||||
{};
|
||||
struct Vector4
|
||||
{
|
||||
float x = 0.0f;
|
||||
float y = 0.0f;
|
||||
float z = 0.0f;
|
||||
float w = 0.0f;
|
||||
|
||||
Vector4() : x(0), y(0), z(0), w(0) {}
|
||||
Vector4(float x, float y, float z, float w) : x(x), y(y), z(z), w(w) {}
|
||||
|
||||
static Vector4 Point(const Vector3& point)
|
||||
{
|
||||
return Vector4(point.x, point.y, point.z, 1.0f);
|
||||
}
|
||||
|
||||
static Vector4 Direction(const Vector3& direction)
|
||||
{
|
||||
return Vector4(direction.x, direction.y, direction.z, 0.0f);
|
||||
}
|
||||
|
||||
Vector3 to_vector3() const
|
||||
{
|
||||
return Vector3(x, y, z);
|
||||
}
|
||||
|
||||
float sqrMagnitude() const
|
||||
{
|
||||
return x * x + y * y + z * z + w * w;
|
||||
}
|
||||
|
||||
float magnitude() const
|
||||
{
|
||||
return std::sqrt(sqrMagnitude());
|
||||
}
|
||||
|
||||
Vector4 normalized() const
|
||||
{
|
||||
const float length = magnitude();
|
||||
if (length <= 0.0f)
|
||||
{
|
||||
return Vector4();
|
||||
}
|
||||
|
||||
return *this / length;
|
||||
}
|
||||
|
||||
float dot(const Vector4& other) const
|
||||
{
|
||||
return x * other.x + y * other.y + z * other.z + w * other.w;
|
||||
}
|
||||
|
||||
Vector4 operator+ (const Vector4& other) const
|
||||
{
|
||||
return Vector4(x + other.x, y + other.y, z + other.z, w + other.w);
|
||||
}
|
||||
|
||||
Vector4 operator- (const Vector4& other) const
|
||||
{
|
||||
return Vector4(x - other.x, y - other.y, z - other.z, w - other.w);
|
||||
}
|
||||
|
||||
Vector4 operator* (float scalar) const
|
||||
{
|
||||
return Vector4(x * scalar, y * scalar, z * scalar, w * scalar);
|
||||
}
|
||||
|
||||
Vector4 operator/ (float scalar) const
|
||||
{
|
||||
return Vector4(x / scalar, y / scalar, z / scalar, w / scalar);
|
||||
}
|
||||
};
|
||||
|
||||
inline Vector4 operator* (float scalar, const Vector4& vector)
|
||||
{
|
||||
return vector * scalar;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,33 @@
|
|||
#pragma once
|
||||
#include "Matrix4x4.h"
|
||||
#include "Camera.h"
|
||||
#include <Vector3.h>
|
||||
|
||||
namespace Scene
|
||||
{
|
||||
Math::Matrix4x4 Camera::get_view_matrix() const
|
||||
{
|
||||
using namespace Math;
|
||||
|
||||
Vector3 forward = (target - position).normalized();
|
||||
Vector3 right = forward.cross(up).normalized();
|
||||
if (right.magnitude() < 1e-5) right = forward.cross(Vector3(0, 1, 0));
|
||||
Vector3 cameraUp = right.cross(forward);
|
||||
|
||||
return Matrix4x4(
|
||||
right.x, right.y, right.z, -right.dot(position),
|
||||
cameraUp.x, cameraUp.y, cameraUp.z, -cameraUp.dot(position),
|
||||
-forward.x, -forward.y, -forward.z, forward.dot(position),
|
||||
0, 0, 0, 1
|
||||
);
|
||||
}
|
||||
|
||||
Math::Matrix4x4 Camera::get_projection_matrix(float aspectRatio) const
|
||||
{
|
||||
using namespace Math;
|
||||
|
||||
return Matrix4x4(
|
||||
|
||||
);
|
||||
}
|
||||
}
|
||||
|
|
@ -1,7 +1,43 @@
|
|||
#pragma once
|
||||
#include "Vector3.h"
|
||||
#include "Matrix4x4.h"
|
||||
|
||||
namespace Scene
|
||||
{
|
||||
class Camera
|
||||
{};
|
||||
{
|
||||
private:
|
||||
Math::Vector3 position = Math::Vector3(0.0f, 0.0f, 0.0f);
|
||||
Math::Vector3 target = Math::Vector3(0.0f, 0.0f, -1.0f);
|
||||
Math::Vector3 up = Math::Vector3(0.0f, 1.0f, 0.0f);
|
||||
|
||||
float verticalFovRadians = 1.0471975512f;
|
||||
float nearPlane = 0.1f;
|
||||
float farPlane = 100.0f;
|
||||
|
||||
public:
|
||||
Camera() = default;
|
||||
|
||||
Math::Vector3 get_position() const { return position; }
|
||||
void set_position(const Math::Vector3& pos) { position = pos; }
|
||||
|
||||
Math::Vector3 get_target() const { return target; }
|
||||
void set_target(const Math::Vector3& t) { target = t; }
|
||||
|
||||
Math::Vector3 get_up() const { return up; }
|
||||
void set_up(const Math::Vector3& u) { up = u; }
|
||||
|
||||
float get_vertical_fov_radians() const { return verticalFovRadians; }
|
||||
void set_vertical_fov_radians(float fov) { verticalFovRadians = fov; }
|
||||
|
||||
float get_near_plane() const { return nearPlane; }
|
||||
void set_near_plane(float nearP) { nearPlane = nearP; }
|
||||
|
||||
float get_far_plane() const { return farPlane; }
|
||||
void set_far_plane(float farP) { farPlane = farP; }
|
||||
|
||||
Math::Matrix4x4 get_view_matrix() const;
|
||||
|
||||
Math::Matrix4x4 get_projection_matrix(float aspectRatio) const;
|
||||
};
|
||||
}
|
||||
Loading…
Reference in New Issue