准备知识

伸缩变换非常简单，它的目的是增大或者缩小对象的尺寸。例如：你可能希望用同一个模型创建不同大小的对象（例如形状相同，但大小不同的树木）或者你想改变对象的大小使它和游戏场景匹配。这些例子中你可能需要X、Y、Z三个坐标轴缩放相同的量，但有时候我们只需要沿着一个或者两个轴缩放使模型变“粗”或变“细”。

缩放变换矩阵形式：



（注：原文没有给出缩放变换矩阵一般形式，此处为本人添加，s1,s2,s3分别为三个轴上的缩放比例）

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

    World.m[1][0] = 0.0f        ; World.m[1][1] = sinf(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] = sinf(Scale); 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 08");

    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

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

World.m[1][0]=0.0f;        World.m[1][1]=sinf(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]=sinf(Scale); 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;

其余代码和上节相同，这里我们把变换矩阵s1,s2,s3的值指定为sinf(Scale),其值域为[-1,1]你将会看到图形一会变大一会变小。

运行效果

编译运行可以看到三角形大小不断改变。