mirror of https://github.com/axmolengine/axmol.git
1006 lines
22 KiB
C++
1006 lines
22 KiB
C++
#include "Mat3.h"
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NS_CC_MATH_BEGIN
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/**
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* Constructor instantiates a new Mat3 object. The initial
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* values for the matrix is that of the identity matrix.
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* 默认构造单位矩阵
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*
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*/
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Mat3::Mat3() {
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loadIdentity();
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}
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/**
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* constructs a matrix with the given values.
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*
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* @param m[0]
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* 0x0 in the matrix.
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* @param m[1]
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* 0x1 in the matrix.
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* @param m[2]
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* 0x2 in the matrix.
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* @param m[3]
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* 1x0 in the matrix.
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* @param m[4]
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* 1x1 in the matrix.
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* @param m[5]
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* 1x2 in the matrix.
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* @param m[6]
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* 2x0 in the matrix.
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* @param m[7]
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* 2x1 in the matrix.
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* @param m[8]
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* 2x2 in the matrix.
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*/
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Mat3::Mat3(float m[9]) {
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this->m[0] = m[0];
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this->m[1] = m[1];
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this->m[2] = m[2];
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this->m[3] = m[3];
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this->m[4] = m[4];
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this->m[5] = m[5];
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this->m[6] = m[6];
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this->m[8] = m[7];
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this->m[9] = m[8];
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}
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/**
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* get retrieves a value from the matrix at the given position.
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* If the position is invalid a JmeException is thrown.
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* 获取指定位置的元素值
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*
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* @param i
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* the row index.行索引（取值范围：0、1、2）
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* @param j
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* the colum index.列索引（取值范围：0、1、2）
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* @return the value at (i, j).
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*/
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float Mat3::get(int i, int j) {
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switch (i) {
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case 0:
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switch (j) {
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case 0:
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return m[0];
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case 1:
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return m[1];
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case 2:
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return m[2];
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}
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case 1:
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switch (j) {
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case 0:
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return m[3];
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case 1:
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return m[4];
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case 2:
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return m[5];
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}
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case 2:
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switch (j) {
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case 0:
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return m[6];
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case 1:
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return m[7];
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case 2:
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return m[8];
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}
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}
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return 0.0f;
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// throw new JmeException("Invalid indices into matrix.");
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}
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/**
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* getColumn returns one of three columns specified by the
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* parameter. This column is returned as a cocos2d::Vec3 object.
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* 获取指定列构造的向量
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*
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* @param i
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* the column to retrieve. Must be between 0 and 2.
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* @param store
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* the vector object to store the result in. if null, a new one
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* is created.
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* @return the column specified by the index.
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*/
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cocos2d::Vec3 Mat3::getColumn(int i) {
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cocos2d::Vec3 store;
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switch (i) {
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case 0:
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store.x = m[0];
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store.y = m[3];
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store.z = m[6];
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break;
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case 1:
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store.x = m[1];
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store.y = m[4];
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store.z = m[7];
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break;
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case 2:
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store.x = m[2];
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store.y = m[5];
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store.z = m[8];
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break;
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default:;
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//logger.warning("Invalid column index.");
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//throw new JmeException("Invalid column index. " + i);
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}
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return store;
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}
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/**
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* getRow returns one of three rows as specified by the
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* parameter. This row is returned as a cocos2d::Vec3 object.
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* 获取指定行构造的向量
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*
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* @param i
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* the row to retrieve. Must be between 0 and 2.
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* @param store
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* the vector object to store the result in. if null, a new one
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* is created.
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* @return the row specified by the index.
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*/
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cocos2d::Vec3 Mat3::getRow(int i) {
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cocos2d::Vec3 store;
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switch (i) {
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case 0:
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store.x = m[0];
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store.y = m[1];
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store.z = m[2];
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break;
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case 1:
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store.x = m[3];
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store.y = m[4];
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store.z = m[5];
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break;
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case 2:
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store.x = m[6];
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store.y = m[7];
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store.z = m[8];
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break;
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default:;
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// throw new JmeException("Invalid row index. " + i);
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}
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return store;
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}
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std::string Mat3::toString() {
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return "";
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}
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/**
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*
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* setColumn sets a particular column of this matrix to that
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* represented by the provided vector.
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* 根据给定列向量设置矩阵的列
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*
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* @param i
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* the column to set.
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* @param column
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* the data to set.
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*/
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void Mat3::setColumn(int i, const cocos2d::Vec3& column) {
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switch (i) {
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case 0:
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m[0] = column.x;
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m[3] = column.y;
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m[6] = column.z;
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break;
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case 1:
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m[1] = column.x;
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m[4] = column.y;
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m[7] = column.z;
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break;
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case 2:
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m[2] = column.x;
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m[5] = column.y;
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m[8] = column.z;
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break;
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default:;
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//logger.warning("Invalid column index.");
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//throw new JmeException("Invalid column index. " + i);
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}
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}
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/**
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*
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* setRow sets a particular row of this matrix to that
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* represented by the provided vector.
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* 根据给定行向量设置矩阵的行
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*
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* @param i
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* the row to set.
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* @param row
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* the data to set.
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*/
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void Mat3::setRow(int i, const cocos2d::Vec3& row) {
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switch (i) {
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case 0:
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m[0] = row.x;
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m[1] = row.y;
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m[2] = row.z;
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break;
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case 1:
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m[3] = row.x;
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m[4] = row.y;
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m[5] = row.z;
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break;
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case 2:
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m[6] = row.x;
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m[7] = row.y;
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m[8] = row.z;
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break;
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default:;
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// logger.warning("Invalid row index.");
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// throw new JmeException("Invalid row index. " + i);
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}
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}
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/**
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* set places a given value into the matrix at the given
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* position. If the position is invalid a JmeException is
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* thrown.
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* 设定某位置的值
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*
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* @param i
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* the row index.
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* @param j
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* the colum index.
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* @param value
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* the value for (i, j).
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*/
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void Mat3::set(int i, int j, float value) {
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switch (i) {
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case 0:
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switch (j) {
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case 0:
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m[0] = value;
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return;
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case 1:
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m[1] = value;
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return;
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case 2:
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m[2] = value;
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return;
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}
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case 1:
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switch (j) {
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case 0:
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m[3] = value;
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return;
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case 1:
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m[4] = value;
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return;
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case 2:
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m[5] = value;
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return;
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}
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case 2:
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switch (j) {
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case 0:
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m[6] = value;
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return;
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case 1:
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m[7] = value;
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return;
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case 2:
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m[8] = value;
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return;
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}
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}
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//logger.warning("Invalid matrix index.");
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//throw new JmeException("Invalid indices into matrix.");
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}
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/**
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*
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* set sets the values of the matrix to those supplied by the
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* 3x3 two dimenion array.
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* 用二维数组设置矩阵各元素值
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*
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* @param matrix
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* the new values of the matrix.
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* @throws JmeException
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* if the array is not of size 9.
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*/
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void Mat3::set(float matrix[3][3]) {
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//if (matrix.length != 3 || matrix[0].length != 3) {
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// throw new JmeException("Array must be of size 9.");
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//}
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m[0] = matrix[0][0];
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m[1] = matrix[0][1];
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m[2] = matrix[0][2];
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m[3] = matrix[1][0];
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m[4] = matrix[1][1];
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m[5] = matrix[1][2];
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m[6] = matrix[2][0];
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m[7] = matrix[2][1];
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m[8] = matrix[2][2];
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}
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/**
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* Recreate Matrix using the provided axis.
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* 根据给定各列向量构造矩阵
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*
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* @param uAxis
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* cocos2d::Vec3
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* @param vAxis
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* cocos2d::Vec3
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* @param wAxis
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* cocos2d::Vec3
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*/
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void Mat3::set(const cocos2d::Vec3& uAxis, const cocos2d::Vec3& vAxis, const cocos2d::Vec3& wAxis) {
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m[0] = uAxis.x;
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m[3] = uAxis.y;
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m[6] = uAxis.z;
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m[1] = vAxis.x;
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m[4] = vAxis.y;
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m[7] = vAxis.z;
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m[2] = wAxis.x;
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m[5] = wAxis.y;
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m[8] = wAxis.z;
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}
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/**
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* set sets the values of this matrix from an array of values;
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* 根据给定数组按行或列设置矩阵
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*
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* @param matrix
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* the matrix to set the value to.
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* @param rowMajor
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* whether the incoming data is in row or column major order.
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*/
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void Mat3::set(float matrix[9], bool rowMajor) {
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//if (matrix.length != 9)
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// throw new JmeException("Array must be of size 9.");
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if (rowMajor) {
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m[0] = matrix[0];
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m[1] = matrix[1];
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m[2] = matrix[2];
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m[3] = matrix[3];
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m[4] = matrix[4];
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m[5] = matrix[5];
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m[6] = matrix[6];
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m[7] = matrix[7];
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m[8] = matrix[8];
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}
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else {
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m[0] = matrix[0];
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m[1] = matrix[3];
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m[2] = matrix[6];
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m[3] = matrix[1];
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m[4] = matrix[4];
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m[5] = matrix[7];
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m[6] = matrix[2];
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m[7] = matrix[5];
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m[8] = matrix[8];
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}
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}
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/**
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* fromAngleNormalAxis sets this matrix4f to the values
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* specified by an angle and a normalized axis of rotation.
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* 绕轴axis（单位向量）旋转angle（弧度）角的3D旋转矩阵
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*
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* @param angle
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* the angle to rotate (in radians).
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* @param axis
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* the axis of rotation (already normalized).
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*/
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/**
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* Creates a matrix describing a rotation around the z-axis.
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*
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* @param angle The angle of rotation (in radians).
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* @param dst A matrix to store the result in.
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*/
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/**
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* Creates a matrix describing a rotation around the y-axis.
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*
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* @param angle The angle of rotation (in radians).
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* @param dst A matrix to store the result in.
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*/
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/**
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* Creates a matrix describing a rotation around the x-axis.
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*
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* @param angle The angle of rotation (in radians).
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* @param dst A matrix to store the result in.
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*/
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/**
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* Creates a matrix describing a rotation around the z-axis.
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*
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* @param angle The angle of rotation (in radians).
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* @param dst A matrix to store the result in.
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*/
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/**
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* Creates a matrix describing a rotation around the y-axis.
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*
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* @param angle The angle of rotation (in radians).
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* @param dst A matrix to store the result in.
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*/
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/**
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* Creates a matrix describing a rotation around the x-axis.
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*
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* @param angle The angle of rotation (in radians).
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* @param dst A matrix to store the result in.
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*/
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/**
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* 是否单位矩阵
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*
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* @return true if this matrix is identity
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*/
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/**
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* loadIdentity sets this matrix to the identity matrix. Where
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* all values are zero except those along the diagonal which are one.
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* 单位矩阵
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*
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*/
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void Mat3::loadIdentity() {
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m[1] = m[2] = m[3] = m[5] = m[6] = m[7] = 0;
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m[0] = m[4] = m[8] = 1;
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}
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bool Mat3::isIdentity() {
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return (m[0] == 1 && m[1] == 0 && m[2] == 0)
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&& (m[3] == 0 && m[4] == 1 && m[5] == 0)
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&& (m[6] == 0 && m[7] == 0 && m[8] == 1);
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}
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void Mat3::rotateX(float angle)
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{
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rotateX(std::sin(angle), std::cos(angle));
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}
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void Mat3::rotateY(float angle)
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{
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rotateY(std::sin(angle), std::cos(angle));
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}
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void Mat3::rotateZ(float angle)
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{
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rotateZ(std::sin(angle), std::cos(angle));
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}
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void Mat3::rotateX(float s, float c)
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{
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Mat3 temp;
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temp.createRotationX(s, c);
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mult(temp);
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}
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void Mat3::rotateY(float s, float c)
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{
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Mat3 temp;
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temp.createRotationY(s, c);
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mult(temp);
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}
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void Mat3::rotateZ(float s, float c)
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{
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Mat3 temp;
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temp.createRotationZ(s, c);
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mult(temp);
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}
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void Mat3::createRotation(const cocos2d::Vec3& axis, float fSin, float fCos) {
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float x = axis.x;
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float y = axis.y;
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float z = axis.z;
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// Make sure the input axis is normalized.
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float n = x * x + y * y + z * z;
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if (n != 1.0f)
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{
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// Not normalized.
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n = sqrt(n);
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// Prevent divide too close to zero.
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if (n > 0.000001f)
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{
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n = 1.0f / n;
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x *= n;
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y *= n;
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z *= n;
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}
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}
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float fOneMinusCos = ((float)1.0) - fCos;
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float fX2 = x * x;
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float fY2 = y * y;
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float fZ2 = z * z;
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float fXYM = x * y * fOneMinusCos;
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float fXZM = x * z * fOneMinusCos;
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float fYZM = y * z * fOneMinusCos;
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float fXSin = x * fSin;
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float fYSin = y * fSin;
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float fZSin = z * fSin;
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m[0] = fX2 * fOneMinusCos + fCos;
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m[1] = fXYM - fZSin;
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m[2] = fXZM + fYSin;
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m[3] = fXYM + fZSin;
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m[4] = fY2 * fOneMinusCos + fCos;
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m[5] = fYZM - fXSin;
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m[6] = fXZM - fYSin;
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m[7] = fYZM + fXSin;
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m[8] = fZ2 * fOneMinusCos + fCos;
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}
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/**
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* Creates a matrix describing a rotation around the x-axis.
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*
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* @param angle The angle of rotation (in radians).
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* @param dst A matrix to store the result in.
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*/
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void Mat3::createRotationX(float s, float c)
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{
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m[4] = c;
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m[5] = s;
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m[7] = -s;
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m[8] = c;
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}
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||
/**
|
||
* Creates a matrix describing a rotation around the y-axis.
|
||
*
|
||
* @param angle The angle of rotation (in radians).
|
||
* @param dst A matrix to store the result in.
|
||
*/
|
||
|
||
void Mat3::createRotationY(float s, float c)
|
||
{
|
||
m[0] = c;
|
||
m[2] = -s;
|
||
m[6] = s;
|
||
m[8] = c;
|
||
}
|
||
|
||
/**
|
||
* Creates a matrix describing a rotation around the z-axis.
|
||
*
|
||
* @param angle The angle of rotation (in radians).
|
||
* @param dst A matrix to store the result in.
|
||
*/
|
||
|
||
void Mat3::createRotationZ(float s, float c)
|
||
{
|
||
m[0] = c;
|
||
m[1] = s;
|
||
m[3] = -s;
|
||
m[4] = c;
|
||
}
|
||
|
||
Mat3& Mat3::mult(const Mat3& mat, Mat3& product) const
|
||
{
|
||
float temp00, temp01, temp02;
|
||
float temp10, temp11, temp12;
|
||
float temp20, temp21, temp22;
|
||
|
||
temp00 = m[0] * mat.m[0] + m[1] * mat.m[3] + m[2] * mat.m[6];
|
||
temp01 = m[0] * mat.m[1] + m[1] * mat.m[4] + m[2] * mat.m[7];
|
||
temp02 = m[0] * mat.m[2] + m[1] * mat.m[5] + m[2] * mat.m[8];
|
||
temp10 = m[3] * mat.m[0] + m[4] * mat.m[3] + m[5] * mat.m[6];
|
||
temp11 = m[3] * mat.m[1] + m[4] * mat.m[4] + m[5] * mat.m[7];
|
||
temp12 = m[3] * mat.m[2] + m[4] * mat.m[5] + m[5] * mat.m[8];
|
||
temp20 = m[6] * mat.m[0] + m[7] * mat.m[3] + m[8] * mat.m[6];
|
||
temp21 = m[6] * mat.m[1] + m[7] * mat.m[4] + m[8] * mat.m[7];
|
||
temp22 = m[6] * mat.m[2] + m[7] * mat.m[5] + m[8] * mat.m[8];
|
||
|
||
product.m[0] = temp00;
|
||
product.m[1] = temp01;
|
||
product.m[2] = temp02;
|
||
product.m[3] = temp10;
|
||
product.m[4] = temp11;
|
||
product.m[5] = temp12;
|
||
product.m[6] = temp20;
|
||
product.m[7] = temp21;
|
||
product.m[8] = temp22;
|
||
|
||
return product;
|
||
}
|
||
|
||
/**
|
||
* Multiplies this 3x3 matrix by the 1x3 Vector vec and stores the result in
|
||
* product.
|
||
* 矩阵乘以向量，结果存入参数product中
|
||
*
|
||
* @param vec
|
||
* The cocos2d::Vec3 to multiply.
|
||
* @return The given product vector.
|
||
*/
|
||
|
||
cocos2d::Vec3 Mat3::mult(const cocos2d::Vec3& vec) const {
|
||
|
||
cocos2d::Vec3 product;
|
||
|
||
float x = vec.x;
|
||
float y = vec.y;
|
||
float z = vec.z;
|
||
|
||
product.x = m[0] * x + m[1] * y + m[2] * z;
|
||
product.y = m[3] * x + m[4] * y + m[5] * z;
|
||
product.z = m[6] * x + m[7] * y + m[8] * z;
|
||
|
||
return product;
|
||
}
|
||
|
||
/**
|
||
* multLocal multiplies this matrix internally by a given float
|
||
* scale factor.
|
||
* 矩阵标量乘
|
||
*
|
||
* @param scale
|
||
* the value to scale by.
|
||
* @return this Mat3
|
||
*/
|
||
|
||
Mat3& Mat3::multLocal(float scale) {
|
||
m[0] *= scale;
|
||
m[1] *= scale;
|
||
m[2] *= scale;
|
||
m[3] *= scale;
|
||
m[4] *= scale;
|
||
m[5] *= scale;
|
||
m[6] *= scale;
|
||
m[7] *= scale;
|
||
m[8] *= scale;
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* add adds the values of a parameter matrix to this matrix.
|
||
* 矩阵加法
|
||
*
|
||
* @param mat
|
||
* the matrix to add to this.
|
||
*/
|
||
|
||
Mat3& Mat3::addLocal(const Mat3& mat) {
|
||
m[0] += mat.m[0];
|
||
m[1] += mat.m[1];
|
||
m[2] += mat.m[2];
|
||
m[3] += mat.m[3];
|
||
m[4] += mat.m[4];
|
||
m[5] += mat.m[5];
|
||
m[6] += mat.m[6];
|
||
m[7] += mat.m[7];
|
||
m[8] += mat.m[8];
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* Transposes this matrix in place. Returns this matrix for chaining
|
||
* 转置矩阵
|
||
*
|
||
* @return This matrix after transpose
|
||
*/
|
||
|
||
Mat3& Mat3::transposeLocal() {
|
||
float tmp[9];
|
||
get(tmp, false);
|
||
set(tmp, true);
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* Inverts this matrix and stores it in the given store.
|
||
* 逆矩阵，保存在参数中，不改变自身
|
||
*
|
||
* @return The store
|
||
*/
|
||
|
||
Mat3 Mat3::invertNew(void) {
|
||
Mat3 store;
|
||
float det = determinant();
|
||
if (std::abs(det) <= 0)
|
||
return store.zero();
|
||
|
||
store.m[0] = m[4] * m[8] - m[5] * m[7];
|
||
store.m[1] = m[2] * m[7] - m[1] * m[8];
|
||
store.m[2] = m[1] * m[5] - m[2] * m[4];
|
||
store.m[3] = m[5] * m[6] - m[3] * m[8];
|
||
store.m[4] = m[0] * m[8] - m[2] * m[6];
|
||
store.m[5] = m[2] * m[3] - m[0] * m[5];
|
||
store.m[6] = m[3] * m[7] - m[4] * m[6];
|
||
store.m[7] = m[1] * m[6] - m[0] * m[7];
|
||
store.m[8] = m[0] * m[4] - m[1] * m[3];
|
||
|
||
store.multLocal(1 / det);
|
||
return store;
|
||
}
|
||
|
||
/**
|
||
* Inverts this matrix locally.
|
||
* 逆矩阵，改变自身
|
||
*
|
||
* @return this
|
||
*/
|
||
|
||
Mat3& Mat3::invertLocal() {
|
||
float det = determinant();
|
||
if (std::abs(det) <= FLT_EPSILON)
|
||
return zero();
|
||
|
||
float f00 = m[4] * m[8] - m[5] * m[7];
|
||
float f01 = m[2] * m[7] - m[1] * m[8];
|
||
float f02 = m[1] * m[5] - m[2] * m[4];
|
||
float f10 = m[5] * m[6] - m[3] * m[8];
|
||
float f11 = m[0] * m[8] - m[2] * m[6];
|
||
float f12 = m[2] * m[3] - m[0] * m[5];
|
||
float f20 = m[3] * m[7] - m[4] * m[6];
|
||
float f21 = m[1] * m[6] - m[0] * m[7];
|
||
float f22 = m[0] * m[4] - m[1] * m[3];
|
||
|
||
m[0] = f00;
|
||
m[1] = f01;
|
||
m[2] = f02;
|
||
m[3] = f10;
|
||
m[4] = f11;
|
||
m[5] = f12;
|
||
m[6] = f20;
|
||
m[7] = f21;
|
||
m[8] = f22;
|
||
|
||
multLocal(1 / det);
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* Places the adjoint of this matrix in store (creates store if null.)
|
||
* 伴随矩阵
|
||
*
|
||
* @param store
|
||
* The matrix to store the result in. If null, a new matrix is
|
||
* created.
|
||
* @return store
|
||
*/
|
||
|
||
Mat3 Mat3::adjoint() {
|
||
Mat3 store;
|
||
|
||
store.m[0] = m[4] * m[8] - m[5] * m[7];
|
||
store.m[1] = m[2] * m[7] - m[1] * m[8];
|
||
store.m[2] = m[1] * m[5] - m[2] * m[4];
|
||
store.m[3] = m[5] * m[6] - m[3] * m[8];
|
||
store.m[4] = m[0] * m[8] - m[2] * m[6];
|
||
store.m[5] = m[2] * m[3] - m[0] * m[5];
|
||
store.m[6] = m[3] * m[7] - m[4] * m[6];
|
||
store.m[7] = m[1] * m[6] - m[0] * m[7];
|
||
store.m[8] = m[0] * m[4] - m[1] * m[3];
|
||
|
||
return store;
|
||
}
|
||
|
||
/**
|
||
* determinant generates the determinate of this matrix.
|
||
* 矩阵的行列式
|
||
*
|
||
* @return the determinate
|
||
*/
|
||
|
||
float Mat3::determinant() {
|
||
float fCo00 = m[4] * m[8] - m[5] * m[7];
|
||
float fCo10 = m[5] * m[6] - m[3] * m[8];
|
||
float fCo20 = m[3] * m[7] - m[4] * m[6];
|
||
float fDet = m[0] * fCo00 + m[1] * fCo10 + m[2] * fCo20;
|
||
return fDet;
|
||
}
|
||
|
||
/**
|
||
* Sets all of the values in this matrix to zero.
|
||
* 重置矩阵，各元素置为0
|
||
*
|
||
* @return this matrix
|
||
*/
|
||
|
||
Mat3& Mat3::zero() {
|
||
m[0] = m[1] = m[2] = m[3] = m[4] = m[5] = m[6] = m[7] = m[8] = 0.0f;
|
||
return *this;
|
||
}
|
||
|
||
/**
|
||
* transposeNew returns a transposed version of this matrix.
|
||
* 转置矩阵
|
||
*
|
||
* @return The new Mat3 object.
|
||
*/
|
||
|
||
Mat3 Mat3::transposeNew() {
|
||
float temp[9] = { m[0], m[3], m[6], m[1], m[4], m[7], m[2], m[5], m[8] };
|
||
return Mat3(temp);
|
||
}
|
||
|
||
/**
|
||
* are these two matrices the same? they are is they both have the same mXX
|
||
* values.
|
||
*
|
||
* @param o
|
||
* the object to compare for equality
|
||
* @return true if they are equal
|
||
*/
|
||
|
||
bool Mat3::equals(const Mat3& o) const {
|
||
return memcmp(&o, this, sizeof(o)) == 0;
|
||
}
|
||
|
||
/**
|
||
* A function for creating a rotation matrix that rotates a vector called
|
||
* "start" into another vector called "end".
|
||
* 创建一个旋转矩阵，从向量start旋转到end
|
||
*
|
||
* @param start
|
||
* normalized non-zero starting vector
|
||
* @param end
|
||
* normalized non-zero ending vector
|
||
* @see "Tomas M?ller, John Hughes /"Efficiently Building a Matrix to Rotate
|
||
* / One Vector to Another/" Journal of Graphics Tools, 4(4):1-4, 1999"
|
||
*/
|
||
|
||
void Mat3::fromStartEndVectors(cocos2d::Vec3 start, cocos2d::Vec3 end) {
|
||
cocos2d::Vec3 v;
|
||
float e, h, f;
|
||
|
||
cocos2d::Vec3::cross(start, end, &v);
|
||
e = start.dot(end);
|
||
f = (e < 0) ? -e : e;
|
||
|
||
// if "from" and "to" vectors are nearly parallel
|
||
if (f > 1.0f - FLT_EPSILON) {
|
||
cocos2d::Vec3 u;
|
||
cocos2d::Vec3 x;
|
||
float c1, c2, c3; /* coefficients for later use */
|
||
int i, j;
|
||
|
||
x.x = (start.x > 0.0) ? start.x : -start.x;
|
||
x.y = (start.y > 0.0) ? start.y : -start.y;
|
||
x.z = (start.z > 0.0) ? start.z : -start.z;
|
||
|
||
if (x.x < x.y) {
|
||
if (x.x < x.z) {
|
||
x.x = 1.0f;
|
||
x.y = x.z = 0.0f;
|
||
}
|
||
else {
|
||
x.z = 1.0f;
|
||
x.x = x.y = 0.0f;
|
||
}
|
||
}
|
||
else {
|
||
if (x.y < x.z) {
|
||
x.y = 1.0f;
|
||
x.x = x.z = 0.0f;
|
||
}
|
||
else {
|
||
x.z = 1.0f;
|
||
x.x = x.y = 0.0f;
|
||
}
|
||
}
|
||
|
||
u.x = x.x - start.x;
|
||
u.y = x.y - start.y;
|
||
u.z = x.z - start.z;
|
||
v.x = x.x - end.x;
|
||
v.y = x.y - end.y;
|
||
v.z = x.z - end.z;
|
||
|
||
c1 = 2.0f / u.dot(u);
|
||
c2 = 2.0f / v.dot(v);
|
||
c3 = c1 * c2 * u.dot(v);
|
||
|
||
for (i = 0; i < 3; i++) {
|
||
for (j = 0; j < 3; j++) {
|
||
float val = -c1 * (&u.x)[i] * (&u.x)[j] - c2 * (&v.x)[i]
|
||
* (&v.x)[j] + c3 * (&v.x)[i] * (&u.x)[j];
|
||
set(i, j, val);
|
||
}
|
||
float val = get(i, i);
|
||
set(i, i, val + 1.0f);
|
||
}
|
||
}
|
||
else {
|
||
// the most common case, unless "start"="end", or "start"=-"end"
|
||
float hvx, hvz, hvxy, hvxz, hvyz;
|
||
h = 1.0f / (1.0f + e);
|
||
hvx = h * v.x;
|
||
hvz = h * v.z;
|
||
hvxy = hvx * v.y;
|
||
hvxz = hvx * v.z;
|
||
hvyz = hvz * v.y;
|
||
set(0, 0, e + hvx * v.x);
|
||
set(0, 1, hvxy - v.z);
|
||
set(0, 2, hvxz + v.y);
|
||
|
||
set(1, 0, hvxy + v.z);
|
||
set(1, 1, e + h * v.y * v.y);
|
||
set(1, 2, hvyz - v.x);
|
||
|
||
set(2, 0, hvxz - v.y);
|
||
set(2, 1, hvyz + v.x);
|
||
set(2, 2, e + hvz * v.z);
|
||
}
|
||
}
|
||
|
||
/**
|
||
* scale scales the operation performed by this matrix on a
|
||
* per-component basis.
|
||
* 标量乘行向量，各列分别相乘
|
||
*
|
||
* @param scale
|
||
* The scale applied to each of the X, Y and Z output values.
|
||
*/
|
||
|
||
void Mat3::scale(const cocos2d::Vec3& scale) {
|
||
m[0] *= scale.x;
|
||
m[3] *= scale.x;
|
||
m[6] *= scale.x;
|
||
m[1] *= scale.y;
|
||
m[4] *= scale.y;
|
||
m[7] *= scale.y;
|
||
m[2] *= scale.z;
|
||
m[5] *= scale.z;
|
||
m[8] *= scale.z;
|
||
}
|
||
|
||
bool Mat3::equalIdentity(const Mat3& mat) {
|
||
if (std::abs(mat.m[0] - 1) > 1e-4)
|
||
return false;
|
||
if (std::abs(mat.m[4] - 1) > 1e-4)
|
||
return false;
|
||
if (std::abs(mat.m[8] - 1) > 1e-4)
|
||
return false;
|
||
|
||
if (std::abs(mat.m[1]) > 1e-4)
|
||
return false;
|
||
if (std::abs(mat.m[2]) > 1e-4)
|
||
return false;
|
||
|
||
if (std::abs(mat.m[3]) > 1e-4)
|
||
return false;
|
||
if (std::abs(mat.m[5]) > 1e-4)
|
||
return false;
|
||
|
||
if (std::abs(mat.m[6]) > 1e-4)
|
||
return false;
|
||
if (std::abs(mat.m[7]) > 1e-4)
|
||
return false;
|
||
|
||
return true;
|
||
}
|
||
|
||
|
||
NS_CC_MATH_END
|