基于C++绘制NURBS曲线生成贝塞尔曲线和B样条曲线（源码+说明文档）.rar

#include "matrix.h" #if 0 // 初始化矩阵(将所有元素初始化为０) void Matrix_Zero(Matrix mat) { int i, j; for (i = 0; i < mat->row; i++) { for (j = 0; j < mat->column; j++) { mat->data[i][j] = 0; } } } void Matrix_Set(Matrix mat, int row, int col, REAL value) { if (row < mat->row && col < mat->column) mat->data[row][col] = value; } //　创建矩阵 Matrix Matrix_CreateZero(int row, int col) { Matrix mat; mat = (Matrix)malloc(sizeof(struct MNode)); //　分配结构体指针 if (row <= 0 || col <= 0) { // printf("ERROR, in creat_Matrix the row or col <= 0\n"); exit(1); } if (row > 0 && col > 0) { mat->row = row; mat->column = col; mat->data = (REAL **)malloc(row * sizeof(REAL *)); // 分配头指针 if (mat->data == NULL) { // printf("ERROR, in creat_Matrix the mat->data == NULL\n"); exit(1); } int i; for (i = 0; i < row; i++) { *(mat->data + i) = (REAL *)malloc(col * sizeof(REAL)); //　分配每行的指针 if (mat->data[i] == NULL) { // printf("ERROR, in create_Matrix the mat->data[i] == NULL\n"); exit(1); } } Matrix_Zero(mat); } return mat; } // 释放申请的矩阵空间 void Matrix_Free(Matrix mat) { for (int i = 0; i < mat->row; i++) free(mat->data[i]); // 释放行指针 free(mat->data); // 释放头指针 free(mat); // 释放结构体指针 } //　创建单位矩阵 Matrix Matrix_CreateEye(int n) { Matrix E; int i, j; if (n <= 0) { // printf("ERROR in Matrix_CreateEye\n"); exit(1); } E = Matrix_CreateZero(n, n); for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { if (i == j) E->data[i][j] = 1; else E->data[i][j] = 0; } } return E; } //　打印矩阵 void Matrix_Show(Matrix mat) { int i, j; // printf("%s\n", s); for (i = 0; i < mat->row; i++) { for (j = 0; j < mat->column; j++) { // printf("%.6f\t", mat->data[i][j]); qDebug() << mat->data[i][j]; } // printf("\n"); qDebug() << "\n"; } // printf("\n"); qDebug() << "\n"; } // 给矩阵每个元素赋值 void Matrix_SetData(Matrix mat, REAL data[]) { int i, j; for (i = 0; i < mat->row; i++) { for (j = 0; j < mat->column; j++) { mat->data[i][j] = data[i * mat->column + j]; } } } //　取出矩阵某行某列的元素 REAL Matrix_At(Matrix mat, int row, int col) { REAL rst; rst = mat->data[row - 1][col - 1]; return rst; } // 矩阵第n行与第m行互换 void Matrix_Swap(Matrix mat, int n, int m) { REAL temp; for (int i = 0; i < mat->column; i++) { temp = mat->data[n - 1][i]; mat->data[n - 1][i] = mat->data[m - 1][i]; mat->data[m - 1][i] = temp; } } //　对一个矩阵进行复制 Matrix Matrix_Copy(Matrix mat) { Matrix copy_mat = Matrix_CreateZero(mat->row, mat->column); for (int i = 0; i < mat->row; i++) { for (int j = 0; j < mat->column; j++) copy_mat->data[i][j] = mat->data[i][j]; } return copy_mat; } //　伴随矩阵 Matrix Matrix_Adjoint(Matrix mat) { // Matrix adj; return mat; } //　矩阵加法 Matrix Matrix_Add(Matrix mat_1, Matrix mat_2) { Matrix rst_mat; if (mat_1->column != mat_2->column) { // printf("ERROR in AddorSub, column !=\n"); exit(1); } if (mat_1->row != mat_2->row) { printf("ERROR in AddorSub, row !=\n"); exit(1); } int i, j; rst_mat = Matrix_CreateZero(mat_1->row, mat_1->column); for (i = 0; i < mat_1->row; i++) { for (j = 0; j < mat_1->column; j++) rst_mat->data[i][j] = mat_1->data[i][j] + mat_2->data[i][j]; } return rst_mat; } // 矩阵的减法 Matrix Matrix_Sub(Matrix mat_1, Matrix mat_2) { Matrix rst_mat; if (mat_1->column != mat_2->column) { // printf("ERROR in AddorSub, column !=\n"); exit(1); } if (mat_1->row != mat_2->row) { printf("ERROR in AddorSub, row !=\n"); exit(1); } int i, j; rst_mat = Matrix_CreateZero(mat_1->row, mat_1->column); for (i = 0; i < mat_1->row; i++) { for (j = 0; j < mat_1->column; j++) rst_mat->data[i][j] = mat_1->data[i][j] - mat_2->data[i][j]; } return rst_mat; } // 矩阵转置 Matrix Matrix_Transpose(Matrix mat) { Matrix mat_; int i, j; mat_ = Matrix_CreateZero(mat->row, mat->column); for (i = 0; i < mat->row; i++) { for (j = 0; j < mat->column; j++) mat_->data[i][j] = mat->data[i][j]; } return mat_; } // 矩阵乘法 Matrix Matrix_Mult(Matrix mat_1, Matrix mat_2) { Matrix rst_mat; int i, j, m; if (mat_1->column != mat_2->row) { // printf("ERROR in Matrix_Mult, column != row\n"); exit(1); } else { rst_mat = Matrix_CreateZero(mat_1->row, mat_2->column); for (i = 0; i < mat_1->row; i++) { for (j = 0; j < mat_2->column; j++) { for (m = 0; m < mat_1->column; m++) rst_mat->data[i][j] += mat_1->data[i][m] * mat_2->data[m][j]; } } } return rst_mat; } // 矩阵乘法常数 Matrix Matrix_MultConst(Matrix mat, float ratio) { int i = 0, j = 0; for (i = 0; i < mat->row; i++) { for (j = 0; j < mat->column; j++) { mat->data[i][j] *= ratio; } } return mat; } // 矩阵求逆，利用矩阵LU分解求逆（直接三角分解） Matrix Matrix_Inverse_LU(Matrix mat) { Matrix inv; if (mat->column != mat->row) { // printf("ERROR in inverse, the row != the column\n"); exit(1); } if (Matrix_Det(mat) == 0) { // printf("The Matrix is not invertible\n"); exit(1); } // Ｌ矩阵和Ｕ矩阵 Matrix L, U; int n = mat->column; inv = Matrix_CreateZero(n, n); L = Matrix_CreateZero(n, n); U = Matrix_CreateZero(n, n); // 计算Ｕ的第一行元素 for (int j = 0; j < n; j++) U->data[0][j] = mat->data[0][j]; //　计算Ｌ的第一列元素 for (int i = 0; i < n; i++) { L->data[i][0] = mat->data[i][0] / U->data[0][0]; L->data[i][i] = 1.0; } REAL sum_u = 0, sum_l = 0; //　分别计算Ｕ和Ｌ的第２到ｎ行、列元素 for (int k = 1; k < n; k++) { // 求U，U矩阵从第２行迭代到第n行，且U矩阵先于L矩阵一个节拍 for (int j = k; j < n; j++) { sum_u = 0; for (int m = 0; m <= k - 1; m++) sum_u += L->data[k][m] * U->data[m][j]; U->data[k][j] = mat->data[k][j] - sum_u; } //　求Ｌ，L矩阵从第２列迭代到第n列 for (int i = k + 1; i < n; i++) { sum_l = 0; for (int m = 0; m <= k - 1; m++) sum_l += L->data[i][m] * U->data[m][k]; L->data[i][k] = (mat->data[i][k] - sum_l) / U->data[k][k]; } } // 分别求下三角矩阵Ｌ和上三角矩阵Ｕ的逆矩阵 Matrix L_, U_; L_ = Matrix_CreateZero(n, n); U_ = Matrix_CreateZero(n, n); // 求矩阵Ｕ的逆 REAL sum_u_; for (int i = 0; i < n; i++) { U_->data[i][i] = 1.0 / U->data[i][i]; // 对角线元素的值直接取倒数 for (int j = i - 1; j >= 0; j--) { sum_u_ = 0; for (int k = j + 1; k <= i; k++)