Math.cpp

#include "Math.h"#include "Camera.h"Cube ::Cube(float x, float y, float z){vertexCount = 8 ;polyCount = 12 ;position.x = x ;position.y = y ;position.z = z ;float scaler = 0.2 ;localVertices[0].x = -50  * scaler ;localVertices[0].y = 50 * scaler ;localVertices[0].z = -50 * scaler ;localVertices[0].w = 1 ;localVertices[1].x = 50 * scaler ;localVertices[1].y = 50 * scaler ;localVertices[1].z = -50 * scaler ;localVertices[1].w = 1 ;localVertices[2].x = 50 * scaler ;localVertices[2].y = -50 * scaler ;localVertices[2].z = -50 * scaler ;localVertices[2].w = 1 ;localVertices[3].x = -50 * scaler ;localVertices[3].y = -50 * scaler ;localVertices[3].z = -50 * scaler ;localVertices[3].w = 1 ;localVertices[4].x = 50 * scaler ;localVertices[4].y = 50 * scaler ;localVertices[4].z = 50 * scaler ;localVertices[4].w = 1 ;localVertices[5].x = 50 * scaler ;localVertices[5].y = -50 * scaler ;localVertices[5].z = 50 * scaler ;localVertices[5].w = 1 ;localVertices[6].x = -50 * scaler ;localVertices[6].y = -50 * scaler ;localVertices[6].z = 50 * scaler ;localVertices[6].w = 1 ;localVertices[7].x = -50 * scaler ;localVertices[7].y = 50 * scaler ;localVertices[7].z = 50 * scaler ;localVertices[7].w = 1 ;polygones[0].pVertexList = transformedVertices ;polygones[0].vertexIndexArray[0] = 0 ;polygones[0].vertexIndexArray[1] = 3 ;polygones[0].vertexIndexArray[2] = 2 ;polygones[1].pVertexList = transformedVertices ;polygones[1].vertexIndexArray[0] = 0 ;polygones[1].vertexIndexArray[1] = 2 ;polygones[1].vertexIndexArray[2] = 1 ;polygones[2].pVertexList = transformedVertices ;polygones[2].vertexIndexArray[0] = 1 ;polygones[2].vertexIndexArray[1] = 2 ;polygones[2].vertexIndexArray[2] = 5 ;polygones[3].pVertexList = transformedVertices ;polygones[3].vertexIndexArray[0] = 1 ;polygones[3].vertexIndexArray[1] = 5 ;polygones[3].vertexIndexArray[2] = 4 ;polygones[4].pVertexList = transformedVertices ;polygones[4].vertexIndexArray[0] = 4 ;polygones[4].vertexIndexArray[1] = 5 ;polygones[4].vertexIndexArray[2] = 6 ;polygones[5].pVertexList = transformedVertices ;polygones[5].vertexIndexArray[0] = 4 ;polygones[5].vertexIndexArray[1] = 6;polygones[5].vertexIndexArray[2] = 7 ;polygones[6].pVertexList = transformedVertices ;polygones[6].vertexIndexArray[0] = 7 ;polygones[6].vertexIndexArray[1] = 6 ;polygones[6].vertexIndexArray[2] = 3 ;polygones[7].pVertexList = transformedVertices ;polygones[7].vertexIndexArray[0] = 7 ;polygones[7].vertexIndexArray[1] = 3 ;polygones[7].vertexIndexArray[2] = 0 ;polygones[8].pVertexList = transformedVertices ;polygones[8].vertexIndexArray[0] = 7 ;polygones[8].vertexIndexArray[1] = 0 ;polygones[8].vertexIndexArray[2] = 1 ;polygones[9].pVertexList = transformedVertices ;polygones[9].vertexIndexArray[0] = 4 ;polygones[9].vertexIndexArray[1] = 7 ;polygones[9].vertexIndexArray[2] = 1 ;polygones[10].pVertexList = transformedVertices ;polygones[10].vertexIndexArray[0] = 3 ;polygones[10].vertexIndexArray[1] = 6 ;polygones[10].vertexIndexArray[2] = 5 ;polygones[11].pVertexList = transformedVertices ;polygones[11].vertexIndexArray[0] = 2 ;polygones[11].vertexIndexArray[1] = 3 ;polygones[11].vertexIndexArray[2] = 5 ;}void Cube ::RotateAroundX(float unit){float sinTheta = sin(DEGREE_TO_RADIAN((unit))) ;float cosTheta = cos(DEGREE_TO_RADIAN((unit))) ;Matrix4X4 rotateAroundY = {1, 0, 0, 0,0, cosTheta, sinTheta, 0,0, -sinTheta, cosTheta, 0,0, 0, 0, 1} ;Vector4 temp ;for (int i = 0; i < vertexCount; ++i){VectorMultMatrix(&localVertices[i], &rotateAroundY, &temp) ;localVertices[i].x = temp.x ;localVertices[i].y = temp.y ;localVertices[i].z = temp.z ;localVertices[i].w = temp.w ;}}void Cube ::RotateAroundY(float unit){float sinTheta = sin(DEGREE_TO_RADIAN((unit))) ;float cosTheta = cos(DEGREE_TO_RADIAN((unit))) ;Matrix4X4 rotateAroundY = {cosTheta, 0, -sinTheta, 0,0, 1, 0, 0,sinTheta, 0, cosTheta, 0,0, 0, 0, 1} ;Vector4 temp ;for (int i = 0; i < vertexCount; ++i){VectorMultMatrix(&localVertices[i], &rotateAroundY, &temp) ;localVertices[i].x = temp.x ;localVertices[i].y = temp.y ;localVertices[i].z = temp.z ;localVertices[i].w = temp.w ;}}void Cube ::RotateAroundZ(float unit){float sinTheta = sin(DEGREE_TO_RADIAN((unit))) ;float cosTheta = cos(DEGREE_TO_RADIAN((unit))) ;Matrix4X4 rotateAroundZ = {cosTheta, sinTheta, 0, 0,-sinTheta, cosTheta, 0, 0,0, 0, 1, 0,0, 0, 0, 1} ;Vector4 temp ;for (int i = 0; i < vertexCount; ++i){VectorMultMatrix(&localVertices[i], &rotateAroundZ, &temp) ;localVertices[i].x = temp.x ;localVertices[i].y = temp.y ;localVertices[i].z = temp.z ;localVertices[i].w = temp.w ;}}void VectorPlusVector(Vector3* lhs, Vector3* rhs, Vector3* pResult){pResult ->x = lhs ->x + rhs ->x ;pResult ->y = lhs ->y + rhs ->y ;pResult ->z = lhs ->z + rhs ->z ;}void VectorMinusVector(Vector3* endPoint, Vector3* startPoint, Vector3* pResult){pResult ->x = endPoint ->x - startPoint ->x ;pResult ->y = endPoint ->y - startPoint ->y ;pResult ->z = endPoint ->z - startPoint ->z ;}void VectorCrossVector(Vector3* lhs, Vector3* rhs, Vector3* pResult){pResult ->x = lhs ->y * rhs ->z - lhs ->z * rhs ->y ;pResult ->y = lhs ->z * rhs ->x - lhs ->x * rhs ->z ;pResult ->z = lhs ->x * rhs ->y - lhs ->y * rhs ->x ;}float VectorDotVector(Vector3* lhs, Vector3* rhs){return lhs ->x * rhs ->x + lhs ->y * rhs ->y + lhs ->z * rhs ->z ;}void Vector4ToVector3(Vector4* resourcePoint, Vector3* newPoint){newPoint ->x = resourcePoint ->x / resourcePoint ->w ;newPoint ->y = resourcePoint ->y / resourcePoint ->w ;newPoint ->z = resourcePoint ->z / resourcePoint ->w ;}void InitializeMatrix(Matrix3X3* pMatrix,float m11, float m12, float m13,float m21, float m22, float m23,float m31, float m32, float m33){pMatrix ->m11 = m11 ; pMatrix ->m12 = m12 ; pMatrix ->m13 = m13 ;pMatrix ->m21 = m21 ; pMatrix ->m22 = m22 ; pMatrix ->m23 = m23 ;pMatrix ->m31 = m31 ; pMatrix ->m32 = m32 ; pMatrix ->m33 = m33 ;}void InitializeMatrix(Matrix4X4* pMatrix,float m11, float m12, float m13, float m14,float m21, float m22, float m23, float m24,float m31, float m32, float m33, float m34,float m41, float m42, float m43, float m44){pMatrix ->m11 = m11 ; pMatrix ->m12 = m12 ; pMatrix ->m13 = m13 ; pMatrix ->m14 = m14 ;pMatrix ->m21 = m21 ; pMatrix ->m22 = m22 ; pMatrix ->m23 = m23 ; pMatrix ->m24 = m24 ;pMatrix ->m31 = m31 ; pMatrix ->m32 = m32 ; pMatrix ->m33 = m33 ; pMatrix ->m34 = m34 ;pMatrix ->m41 = m41 ; pMatrix ->m42 = m42 ; pMatrix ->m43 = m43 ; pMatrix ->m44 = m44 ;}void VectorMultMatrix(Vector4* point, Matrix4X4* matrix, Vector4* pResult){for (int col = 0; col < 4; ++col){float sum = 0 ;for (int row = 0; row < 4; ++row)sum += point ->M[row] * matrix ->M[row][col] ;pResult ->M[col] = sum ;}}void MatrixMultMatrix(Matrix4X4* lhs, Matrix4X4* rhs, Matrix4X4* pResult){for (int row = 0; row < 4; ++row){for (int col = 0; col < 4; ++col){float temp = 0 ;for (int i = 0; i < 4; ++i)temp += lhs ->M[row][i] * rhs ->M[i][col] ;pResult ->M[row][col] = temp ;}}}float GetDeterminant(const Matrix4X4* pMatrix){return pMatrix ->m11 * pMatrix ->m22 * pMatrix ->m33 * pMatrix ->m44 - pMatrix ->m11 * pMatrix ->m24 * pMatrix ->m33 * pMatrix ->m42+ pMatrix ->m12 * pMatrix ->m23 * pMatrix ->m34 * pMatrix ->m41 - pMatrix ->m12 * pMatrix ->m21 * pMatrix ->m34 * pMatrix ->m43+ pMatrix ->m13 * pMatrix ->m24 * pMatrix ->m31 * pMatrix ->m42 - pMatrix ->m13 * pMatrix ->m22 * pMatrix ->m31 * pMatrix ->m44+ pMatrix ->m14 * pMatrix ->m21 * pMatrix ->m32 * pMatrix ->m43 - pMatrix ->m14 * pMatrix ->m23 * pMatrix ->m32 * pMatrix ->m41 ;}void ScaleAccordingTo(Cube* pCube, Vector3* pAxis, float k){Matrix4X4 matrix = {1 + (k - 1) * pAxis ->x * pAxis ->x, (k - 1) * pAxis ->x * pAxis ->y, (k - 1) * pAxis ->x * pAxis ->z, 0, (k - 1) * pAxis ->x * pAxis ->y, 1 + (k - 1) * pAxis ->y * pAxis ->y, (k - 1) * pAxis ->y * pAxis ->z, 0, (k - 1) * pAxis ->x * pAxis ->z, (k - 1) * pAxis ->z * pAxis ->y, 1 + (k - 1) * pAxis ->z * pAxis ->z, 0,0, 0, 0, 1} ;for (int i = 0; i < pCube ->vertexCount; ++i)VectorMultMatrix(&pCube ->localVertices[i], &matrix, &pCube ->localVertices[i]) ;}void ModelToWorld(Cube* pCube){for (int i = 0; i < pCube ->vertexCount; ++i){pCube ->transformedVertices[i].x = pCube ->localVertices[i].x + pCube ->position.x ;pCube ->transformedVertices[i].y = pCube ->localVertices[i].y + pCube ->position.y ;pCube ->transformedVertices[i].z = pCube ->localVertices[i].z + pCube ->position.z ;pCube ->transformedVertices[i].w = pCube ->localVertices[i].w ;}}void RemoveBackface(PolySelfContained* polyList, int count, Vector3* pViewPortPosition){for (int i = 0; i < count; ++i){Vector3 point0 ;point0.x = polyList[i].vertexList[0].x ;point0.y = polyList[i].vertexList[0].y ;point0.z = polyList[i].vertexList[0].z ;Vector3 point1 ;point1.x = polyList[i].vertexList[1].x ;point1.y = polyList[i].vertexList[1].y ;point1.z = polyList[i].vertexList[1].z ;Vector3 point2 ;point2.x = polyList[i].vertexList[2].x ;point2.y = polyList[i].vertexList[2].y ;point2.z = polyList[i].vertexList[2].z ;//  1//  /// ////// 0\// \//    \//     \//      2Vector3 u ;VectorMinusVector(&point1, &point0, &u) ;Vector3 v ;VectorMinusVector(&point2, &point0, &v) ;Vector3 n ;VectorCrossVector(&v, &u, &n) ;Vector3 view ;VectorMinusVector(pViewPortPosition, &point0, &view) ;float dotValue = VectorDotVector(&n, &view) ;if (dotValue <= 0)polyList[i].removed = true ;elsepolyList[i].removed = false ;}}void WorldToCamera(PolySelfContained* polyList, int count, Matrix4X4* pMatrix){Vector4 temp ;for (int i = 0; i < count; ++i){if (polyList[i].removed)continue ;VectorMultMatrix(&polyList[i].vertexList[0], pMatrix, &temp) ;polyList[i].vertexList[0] = temp;VectorMultMatrix(&polyList[i].vertexList[1], pMatrix, &temp) ;polyList[i].vertexList[1]= temp ;VectorMultMatrix(&polyList[i].vertexList[2], pMatrix, &temp) ;polyList[i].vertexList[2] = temp ;}}void CameraToClip(PolySelfContained* polyList, int count, Matrix4X4* pMatrix){Vector4 temp ;for (int i = 0; i < count; ++i){if (polyList[i].removed)continue ;VectorMultMatrix(&polyList[i].vertexList[0], pMatrix, &temp) ;polyList[i].vertexList[0] = temp ;VectorMultMatrix(&polyList[i].vertexList[1], pMatrix, &temp) ;polyList[i].vertexList[1]= temp ;VectorMultMatrix(&polyList[i].vertexList[2], pMatrix, &temp) ;polyList[i].vertexList[2] = temp ;}}void ClipToPerspective(PolySelfContained* polyList, int count, float nearDistance){for (int i = 0; i < count; ++i){if (polyList[i].removed)continue ;float w = polyList[i].vertexList[0].w ;polyList[i].vertexList[0].x /= w ;polyList[i].vertexList[0].y /= w ;polyList[i].vertexList[0].z = nearDistance ;w = polyList[i].vertexList[1].w ;polyList[i].vertexList[1].x /= w ;polyList[i].vertexList[1].y /= w ;polyList[i].vertexList[1].z = nearDistance ;w = polyList[i].vertexList[2].w ;polyList[i].vertexList[2].x /= w ;polyList[i].vertexList[2].y /= w ;polyList[i].vertexList[2].z = nearDistance ;}}void CameraToperspective(PolySelfContained* polyList, int count, float viewPortWidth, float viewPortHeight, float fov){float viewDistance = (viewPortWidth - 1) / 2 / tan(fov / 2) ;Matrix4X4 projectionMatrix = {1, 0, 0, 0,0, 1, 0, 0,0, 0, 1, 1 / viewDistance,0, 0, 0, 0} ;Vector4 temp ;for (int i = 0; i < count; ++i){if (polyList[i].removed)continue ;VectorMultMatrix(&polyList[i].vertexList[0], &projectionMatrix, &temp) ;polyList[i].vertexList[0] = temp ;polyList[i].vertexList[0].x /= polyList[i].vertexList[0].w ;polyList[i].vertexList[0].y /= polyList[i].vertexList[0].w ;polyList[i].vertexList[0].z /= polyList[i].vertexList[0].w ;VectorMultMatrix(&polyList[i].vertexList[1], &projectionMatrix, &temp) ;polyList[i].vertexList[1] = temp ;polyList[i].vertexList[1].x /= polyList[i].vertexList[1].w ;polyList[i].vertexList[1].y /= polyList[i].vertexList[1].w ;polyList[i].vertexList[1].z /= polyList[i].vertexList[1].w ;VectorMultMatrix(&polyList[i].vertexList[2], &projectionMatrix, &temp) ;polyList[i].vertexList[2] = temp ;polyList[i].vertexList[2].x /= polyList[i].vertexList[2].w ;polyList[i].vertexList[2].y /= polyList[i].vertexList[2].w ;polyList[i].vertexList[2].z /= polyList[i].vertexList[2].w ;}}void PerspectiveToScreen(PolySelfContained* polyList, int count, float viewPortWidth, float viewPortHeight){Vector4 temp ;for (int i = 0; i < count; ++i){if (polyList[i].removed)continue ;//polyList[i].vertexList[0].x = viewPortWidth * (polyList[i].vertexList[0].x + 1) / 2 ;//polyList[i].vertexList[0].y = viewPortHeight * (polyList[i].vertexList[0].y + 1) / 2 ;//polyList[i].vertexList[1].x = viewPortWidth * (polyList[i].vertexList[1].x + 1) / 2 ;//polyList[i].vertexList[1].y = viewPortHeight * (polyList[i].vertexList[1].y + 1) / 2 ;//polyList[i].vertexList[2].x = viewPortWidth * (polyList[i].vertexList[2].x + 1) / 2 ;//polyList[i].vertexList[2].y = viewPortHeight * (polyList[i].vertexList[2].y + 1) / 2 ;polyList[i].vertexList[0].x = (polyList[i].vertexList[0].x + 1) * (viewPortWidth / 2 - 0.5) ;polyList[i].vertexList[0].y = (viewPortHeight - 1) - (polyList[i].vertexList[0].y + 1) * (viewPortHeight / 2 - 0.5) ;polyList[i].vertexList[1].x = (polyList[i].vertexList[1].x + 1) * (viewPortWidth / 2 - 0.5) ;polyList[i].vertexList[1].y = (viewPortHeight - 1) - (polyList[i].vertexList[1].y + 1) * (viewPortHeight / 2 - 0.5) ;polyList[i].vertexList[2].x = (polyList[i].vertexList[2].x + 1) * (viewPortWidth / 2 - 0.5) ;polyList[i].vertexList[2].y = (viewPortHeight - 1) - (polyList[i].vertexList[2].y + 1) * (viewPortHeight / 2 - 0.5) ;//temp.x = viewPortWidth / 2 - 0.5 + polyList[i].vertexList[0].x ;//temp.y = viewPortHeight / 2 - 0.5 - polyList[i].vertexList[0].y ;//temp.z = polyList[i].vertexList[0].z ;//temp.w = polyList[i].vertexList[0].w ;//polyList[i].vertexList[0] = temp ;//temp.x = viewPortWidth / 2 - 0.5 + polyList[i].vertexList[1].x ;//temp.y = viewPortHeight / 2 - 0.5 - polyList[i].vertexList[1].y ;//temp.z = polyList[i].vertexList[1].z ;//temp.w = polyList[i].vertexList[1].w ;//polyList[i].vertexList[1] = temp ;//temp.x = viewPortWidth / 2 - 0.5 + polyList[i].vertexList[2].x ;//temp.y = viewPortHeight / 2 - 0.5 - polyList[i].vertexList[2].y ;//temp.z = polyList[i].vertexList[2].z ;//temp.w = polyList[i].vertexList[2].w ;//polyList[i].vertexList[2] = temp ;}}