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
", 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'
", ShaderType, InfoLog);
        exit(1);
    }

    glAttachShader(ShaderProgram, ShaderObj);
}

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

    if (ShaderProgram == 0) {
        fprintf(stderr, "Error creating shader program
");
        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'
", 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'
", 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'
", glewGetErrorString(res));
        return 1;
    }

    printf("GL version: %s
", 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。