OpenGL编程逐步深入（七）旋转变换

准备知识

这一节我们来看一下旋转变换。旋转变换指的是给我们一个指点的点和角度，我们需要绕着过该点的轴线將对象旋转对应的角度。这里我们只改变X/Y/Z中的两个分量，第三个分量保持不变。这意味着我们的图形只在三个平面内旋转：XY平面（绕着Z轴）、YZ平面（绕着X轴）、XZ（绕着Y轴）。还有更复杂的旋转方式这里我们暂时用不到。

我们来概括性的定义这个问题。考虑下面这样的图形：



我们需要沿着圆把点（x1,y2）移动到（x2,y2），换句话说就是把（x1,y1）旋转a2角度。我们假定圆的半径为1，则有：



使用正余弦展开公式：



可得：



在上面的图形中，Z轴垂直于屏幕，XY平面和屏幕重合。和平移变换一样，我们4x4阶矩阵和顶点分量矩阵乘积的形式表示该变换，可以写成：



绕Y轴选择可以用以下形式表示：



绕X轴旋转：



上面的4x4阶矩阵就是我们的旋转变换矩阵。

程序代码

/*

Copyright 2010 Etay Meiri

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <http://www.gnu.org/licenses/>.

Tutorial 07 - Rotation transformation
*/
#include "stdafx.h"
#include <stdio.h>
#include <string.h>
#include <assert.h>
#include <math.h>
#include <GL/glew.h>
#include <GL/freeglut.h>
#include "ogldev_math_3d.h"
GLuint VBO;
GLuint gWorldLocation;

const char* pVSFileName = "shader.vs";
const char* pFSFileName = "shader.fs";

static void RenderSceneCB()
{
glClear(GL_COLOR_BUFFER_BIT);

static float Scale = 0.0f;

Scale += 0.001f;

Matrix4f World;

World.m[0][0] = cosf(Scale); World.m[0][1] = -sinf(Scale); World.m[0][2] = 0.0f; World.m[0][3] = 0.0f;
World.m[1][0] = sinf(Scale); World.m[1][1] = cosf(Scale);  World.m[1][2] = 0.0f; World.m[1][3] = 0.0f;
World.m[2][0] = 0.0f;        World.m[2][1] = 0.0f;         World.m[2][2] = 1.0f; World.m[2][3] = 0.0f;
World.m[3][0] = 0.0f;        World.m[3][1] = 0.0f;         World.m[3][2] = 0.0f; World.m[3][3] = 1.0f;

glUniformMatrix4fv(gWorldLocation, 1, GL_TRUE, &World.m[0][0]);

glEnableVertexAttribArray(0);
glBindBuffer(GL_ARRAY_BUFFER, VBO);
glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 0, 0);

glDrawArrays(GL_TRIANGLES, 0, 3);

glDisableVertexAttribArray(0);

glutSwapBuffers();
}

static void InitializeGlutCallbacks()
{
glutDisplayFunc(RenderSceneCB);
glutIdleFunc(RenderSceneCB);
}

static void CreateVertexBuffer()
{
Vector3f Vertices[3];
Vertices[0] = Vector3f(-1.0f, -1.0f, 0.0f);
Vertices[1] = Vector3f(1.0f, -1.0f, 0.0f);
Vertices[2] = Vector3f(0.0f, 1.0f, 0.0f);

glGenBuffers(1, &VBO);
glBindBuffer(GL_ARRAY_BUFFER, VBO);
glBufferData(GL_ARRAY_BUFFER, sizeof(Vertices), Vertices, GL_STATIC_DRAW);
}

static void AddShader(GLuint ShaderProgram, const char* pShaderText, GLenum ShaderType)
{
GLuint ShaderObj = glCreateShader(ShaderType);

if (ShaderObj == 0) {
fprintf(stderr, "Error creating shader type %d\n", ShaderType);
exit(1);
}

const GLchar* p[1];
p[0] = pShaderText;
GLint Lengths[1];
Lengths[0]= strlen(pShaderText);
glShaderSource(ShaderObj, 1, p, Lengths);
glCompileShader(ShaderObj);
GLint success;
glGetShaderiv(ShaderObj, GL_COMPILE_STATUS, &success);
if (!success) {
GLchar InfoLog[1024];
glGetShaderInfoLog(ShaderObj, 1024, NULL, InfoLog);
fprintf(stderr, "Error compiling shader type %d: '%s'\n", ShaderType, InfoLog);
exit(1);
}

glAttachShader(ShaderProgram, ShaderObj);
}

static void CompileShaders()
{
GLuint ShaderProgram = glCreateProgram();

if (ShaderProgram == 0) {
fprintf(stderr, "Error creating shader program\n");
exit(1);
}
string vs, fs;

if (!ReadFile(pVSFileName, vs)) {
exit(1);
};

if (!ReadFile(pFSFileName, fs)) {
exit(1);
};

AddShader(ShaderProgram, vs.c_str(), GL_VERTEX_SHADER);
AddShader(ShaderProgram, fs.c_str(), GL_FRAGMENT_SHADER);

GLint Success = 0;
GLchar ErrorLog[1024] = { 0 };

glLinkProgram(ShaderProgram);
glGetProgramiv(ShaderProgram, GL_LINK_STATUS, &Success);
if (Success == 0) {
glGetProgramInfoLog(ShaderProgram, sizeof(ErrorLog), NULL, ErrorLog);
fprintf(stderr, "Error linking shader program: '%s'\n", ErrorLog);
exit(1);
}

glValidateProgram(ShaderProgram);
glGetProgramiv(ShaderProgram, GL_VALIDATE_STATUS, &Success);
if (!Success) {
glGetProgramInfoLog(ShaderProgram, sizeof(ErrorLog), NULL, ErrorLog);
fprintf(stderr, "Invalid shader program: '%s'\n", ErrorLog);
exit(1);
}

glUseProgram(ShaderProgram);

gWorldLocation = glGetUniformLocation(ShaderProgram, "gWorld");
assert(gWorldLocation != 0xFFFFFFFF);
}
int _tmain(int argc, _TCHAR* argv[])
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DOUBLE|GLUT_RGBA);
glutInitWindowSize(1024, 768);
glutInitWindowPosition(100, 100);
glutCreateWindow("Tutorial 07");

InitializeGlutCallbacks();

// Must be done after glut is initialized!
GLenum res = glewInit();
if (res != GLEW_OK) {
fprintf(stderr, "Error: '%s'\n", glewGetErrorString(res));
return 1;
}

printf("GL version: %s\n", glGetString(GL_VERSION));

glClearColor(0.0f, 0.0f, 0.0f, 0.0f);

CreateVertexBuffer();

CompileShaders();

glutMainLoop();

return 0;
}

代码解读

这里我们只把矩阵改成旋转变换矩阵，其余代码和上节相同。

World.m[0][0]=cosf(Scale); World.m[0][1]=-sinf(Scale); World.m[0][2]=0.0f; World.m[0][3]=0.0f;
World.m[1][0]=sinf(Scale); World.m[1][1]=cosf(Scale);  World.m[1][2]=0.0f; World.m[1][3]=0.0f;
World.m[2][0]=0.0f;        World.m[2][1]=0.0f;         World.m[2][2]=1.0f; World.m[2][3]=0.0f;
World.m[3][0]=0.0f;        World.m[3][1]=0.0f;         World.m[3][2]=0.0f; World.m[3][3]=1.0f;

运行效果

可以看到三角形在屏幕上不停旋转。