2

我试图让一个基本的 OpenGL 程序正常工作。我创建了两种方法来创建模型视图矩阵（目前非常初级，它只在 Z 轴上移动我的对象）和投影矩阵。

我的问题是，据我了解 OpenGL，我的投影矩阵应该将具有正 Z 坐标的顶点放置在屏幕上，而将具有负坐标的顶点放置在屏幕后面。

但我的经验是，如果我想要显示它，我需要将我绘制的立方体移动到负 z 方向。你能解释一下，这是为什么吗？我哪里错了？还是我的代码有错误？

我使用这个函数来创建我的投影矩阵：

void Perspective(float *a, float fov, float aspect, float zNear, float zFar)
{
    for(int i = 0; i < 16; i++)
        a[i] = 0.0f;

    float f = 1.0f/float(tan(fov / 2.0f * (M_PI / 180.0f)));

    a[0 + 4 * 0] = f / aspect;
    a[1 + 4 * 1] = f;
    a[2 + 4 * 2] = (zNear + zFar) / (zNear - zFar);
    a[2 + 4 * 3] = 2.0f * zNear *+ zFar / (zNear - zFar);
    a[3 + 4 * 2] = -1.0f;
}

而这个模型视图（我传递不同的偏移量，它们在 0 左右摆动，z 在 -2 左右摆动）：

void Modelview(float *mv, float scale, float xOff, float yOff, float zOff)
{
    for(int i = 0; i < 16; i++)
        mv[i] = 0.0f;

    mv[0 + 4 * 0] = scale;
    mv[0 + 4 * 3] = xOff;
    mv[1 + 4 * 1] = scale;
    mv[1 + 4 * 3] = yOff;
    mv[2 + 4 * 2] = scale;
    mv[2 + 4 * 3] = zOff;
    mv[3 + 4 * 3] = 1.0f;
}

矩阵都正确传递给opengl，我通过以下方式计算顶点位置：

gl_Position = modelview * projection * vertex_position;

这是整个代码，以防有人需要它：

主文件

#include <stdio.h>
#include <cmath>
#include <cstring>
#include <string>
#include <vector>
#include <algorithm>
#include <GL/glew.h>
#include <GL/glut.h>

#include "util.h"

GLuint positionBufferObject, program;
GLint projectionLoc, modelviewLoc, vertexLoc, colorLoc;
float zNear = 0.1f, zFar = 100.0f;
float projection[16], modelview[16];

const Vertex vertices[] =
{
    Vertex(
                Vector4f(0.25f,  0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 0.0f, 1.0f, 1.0f)),
        Vertex(
                Vector4f(0.25f,  -0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 0.0f, 1.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f,  0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 0.0f, 1.0f, 1.0f)),

        Vertex(
                Vector4f(0.25f,  -0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 0.0f, 1.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f,  -0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 0.0f, 1.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f,  0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 0.0f, 1.0f, 1.0f)),

        Vertex(
                Vector4f(0.25f, 0.25f, -0.25f, 1.0f),
                ColorRGBA(0.8f, 0.8f, 0.8f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, 0.25f, -0.25f, 1.0f),
                ColorRGBA(0.8f, 0.8f, 0.8f, 1.0f)),
        Vertex(
                Vector4f(0.25f, -0.25f, -0.25f, 1.0f),
                ColorRGBA(0.8f, 0.8f, 0.8f, 1.0f)),

        Vertex(
                Vector4f(0.25f, -0.25f, -0.25f, 1.0f),
                ColorRGBA(0.8f, 0.8f, 0.8f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, 0.25f, -0.25f, 1.0f),
                ColorRGBA(0.8f, 0.8f, 0.8f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, -0.25f, -0.25f, 1.0f),
                ColorRGBA(0.8f, 0.8f, 0.8f, 1.0f)),

        Vertex(
                Vector4f(-0.25f, 0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, -0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, -0.25f, -0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 0.0f, 1.0f)),

        Vertex(
                Vector4f(-0.25f, 0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, -0.25f, -0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, 0.25f, -0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 0.0f, 1.0f)),

        Vertex(
                Vector4f(0.25f,  0.25f, 0.25f, 1.0f),
                ColorRGBA(0.5f, 0.5f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(0.25f, -0.25f, -0.25f, 1.0f),
                ColorRGBA(0.5f, 0.5f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(0.25f, -0.25f, 0.25f, 1.0f),
                ColorRGBA(0.5f, 0.5f, 0.0f, 1.0f)),

        Vertex(
                Vector4f(0.25f, 0.25f, 0.25f, 1.0f),
                ColorRGBA(0.5f, 0.5f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(0.25f, 0.25f, -0.25f, 1.0f),
                ColorRGBA(0.5f, 0.5f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(0.25f, -0.25f, -0.25f, 1.0f),
                ColorRGBA(0.5f, 0.5f, 0.0f, 1.0f)),

        Vertex(
                Vector4f(0.25f, 0.25f, -0.25f, 1.0f),
                ColorRGBA(1.0f, 0.0f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(0.25f,  0.25f, 0.25f, 1.0f),
                ColorRGBA(1.0f, 0.0f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, 0.25f, 0.25f, 1.0f),
                ColorRGBA(1.0f, 0.0f, 0.0f, 1.0f)),

        Vertex(
                Vector4f(0.25f, 0.25f, -0.25f, 1.0f),
                ColorRGBA(1.0f, 0.0f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, 0.25f, 0.25f, 1.0f),
                ColorRGBA(1.0f, 0.0f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, 0.25f, -0.25f, 1.0f),
                ColorRGBA(1.0f, 0.0f, 0.0f, 1.0f)),

        Vertex(
                Vector4f(0.25f, -0.25f, -0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 1.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, -0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 1.0f, 1.0f)),
        Vertex(
                Vector4f(0.25f, -0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 1.0f, 1.0f)),

        Vertex(
                Vector4f(0.25f, -0.25f, -0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 1.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, -0.25f, -0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 1.0f, 1.0f)),
        Vertex(
                Vector4f(-0.25f, -0.25f, 0.25f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 1.0f, 1.0f)),

        Vertex(
                Vector4f(-1.0f, 0, -1.0f, 1.0f),
                ColorRGBA(1.0f, 0.0f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(0.0f, 1.0, -1.0f, 1.0f),
                ColorRGBA(0.0f, 1.0f, 0.0f, 1.0f)),
        Vertex(
                Vector4f(1.0f, 0, -1.0f, 1.0f),
                ColorRGBA(0.0f, 0.0f, 1.0f, 1.0f))
};

const float vertexData[] =
{
     0.0f,    0.5f, 0.0f, 1.0f,
     0.5f, -0.366f, 0.0f, 1.0f,
    -0.5f, -0.366f, 0.0f, 1.0f,
     1.0f,    0.0f, 0.0f, 1.0f,
     0.0f,    1.0f, 0.0f, 1.0f,
     0.0f,    0.0f, 1.0f, 1.0f,
};

std::string strVertexShader = "simple.vert";

std::string strFragmentShader = "simple.frag";

void init();

void display();

void resize(int w, int h);

void InitializeProgram();

void InitializeVertexBuffer();

void InitializeGlutCallbacks();

void Perspective(float *a, float fov, float aspect, float zNear, float zFar);

void Modelview(float *mv, float scale, float xOff, float yOff, float zOff);

void ComputePositionOffsets(float &fXOffset, float &fYOffset, float &fZOffset, float &scale);

void PrintMat4(float *mat);

主文件

#include "main.h"

int main(int argc, char **argv)
{
    glutInit(&argc, argv);

        glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGBA | GLUT_DEPTH);
        glutInitWindowSize(640, 480);
        glutInitWindowPosition(100, 100);
        glutCreateWindow("Test");

        GLenum res = glewInit();
        if(res != GLEW_OK)
        {
                fprintf(stderr, "Error: '%s'\n", glewGetErrorString(res));
                return -1;
        }

        init();

        glutMainLoop();

        return 0;
}

void display()
{
        glClearColor(0.0f, 0.0f, 0.0f, 0.0f);
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

        float fXOffset = 0.0f, fYOffset = 0.0f, fZOffset = 0.0f, scale = 0.0f;
        ComputePositionOffsets(fXOffset, fYOffset, fZOffset, scale);

        Modelview(modelview, scale, fXOffset, fYOffset, -2.0f + fZOffset);

        glUseProgram(program);

        glUniformMatrix4fv(projectionLoc, 1, GL_FALSE, &projection[0]);
        glUniformMatrix4fv(modelviewLoc, 1, GL_FALSE, &modelview[0]);

        glBindBuffer(GL_ARRAY_BUFFER, positionBufferObject);

        glEnableVertexAttribArray(vertexLoc);
        glEnableVertexAttribArray(colorLoc);

        glVertexAttribPointer(vertexLoc, sizeof(Vector4f)/sizeof(float), GL_FLOAT, GL_FALSE, sizeof(Vertex), (void*)0);
        glVertexAttribPointer(colorLoc, sizeof(ColorRGBA)/sizeof(float), GL_FLOAT, GL_FALSE, sizeof(Vertex), (void*)(sizeof(Vertex)/2));

        glDrawArrays(GL_TRIANGLES, 0, sizeof(vertices)/sizeof(Vertex));

        glDisableVertexAttribArray(vertexLoc);
        glDisableVertexAttribArray(colorLoc);

        glUseProgram(0);

        glutSwapBuffers();
        glutPostRedisplay();
}

void resize(int w, int h)
{
        glViewport(0, 0, w, h);
        Perspective(projection, 90.0f, float(w)/float(h), zNear, zFar);
        PrintMat4(projection);
}

void InitializeProgram()
{
        std::vector<GLuint> shaderList;

        shaderList.push_back(CreateShader(GL_VERTEX_SHADER, strVertexShader));
        shaderList.push_back(CreateShader(GL_FRAGMENT_SHADER, strFragmentShader));

        program = CreateProgram(shaderList);

        vertexLoc = glGetAttribLocation(program, "vertex_position");
        colorLoc = glGetAttribLocation(program, "vertex_color");

        modelviewLoc = glGetUniformLocation(program, "modelview");
        projectionLoc = glGetUniformLocation(program, "projection");

        std::for_each(shaderList.begin(), shaderList.end(), glDeleteShader);
}

void InitializeVertexBuffer()
{
        glGenBuffers(1, &positionBufferObject);

        glBindBuffer(GL_ARRAY_BUFFER, positionBufferObject);
        glBufferData(GL_ARRAY_BUFFER, sizeof(vertices), vertices, GL_STATIC_DRAW);
        glBindBuffer(GL_ARRAY_BUFFER, 0);
}

void InitializeGlutCallbacks()
{
        glutDisplayFunc(display);
        glutReshapeFunc(resize);
}

void init()
{
        InitializeProgram();
        InitializeVertexBuffer();

        InitializeGlutCallbacks();

        glEnable(GL_CULL_FACE);
        glCullFace(GL_BACK);
        glFrontFace(GL_CW);

        glEnable(GL_DEPTH_TEST);
}

void Perspective(float *a, float fov, float aspect, float zNear, float zFar)
{
        for(int i = 0; i < 16; i++)
                a[i] = 0.0f;

        float f = 1.0f/float(tan(fov / 2.0f * (M_PI / 180.0f)));

        a[0 + 4 * 0] = f / aspect;
        a[1 + 4 * 1] = f;
        a[2 + 4 * 2] = (zNear + zFar) / (zNear - zFar);
        a[2 + 4 * 3] = 2.0f * zNear *+ zFar / (zNear - zFar);
        a[3 + 4 * 2] = -1.0f;
}

void Modelview(float *mv, float scale, float xOff, float yOff, float zOff)
{
        for(int i = 0; i < 16; i++)
                mv[i] = 0.0f;

        mv[0 + 4 * 0] = scale;
        mv[0 + 4 * 3] = xOff;
        mv[1 + 4 * 1] = scale;
        mv[1 + 4 * 3] = yOff;
        mv[2 + 4 * 2] = scale;
        mv[2 + 4 * 3] = zOff;
        mv[3 + 4 * 3] = 1.0f;
}

void ComputePositionOffsets(float &fXOffset, float &fYOffset, float &fZOffset, float &scale)
{
        float elapsedTime = glutGet(GLUT_ELAPSED_TIME) / 1000.0f;
        float timeScale = 3.14159f * 2.0f;

        float xLoopDuration = 8.0f;
        float yLoopDuration = 3.0f;
        float zLoopDuration = 2.0f;
        float scaleLoopDuration = 10.0f;
        float xLoopProgress = fmodf(elapsedTime, xLoopDuration) / xLoopDuration;
        float yLoopProgress = fmodf(elapsedTime, yLoopDuration) / yLoopDuration;
        float zLoopProgress = fmodf(elapsedTime, zLoopDuration) / zLoopDuration;
        float scaleLoopProgress = fmodf(elapsedTime, scaleLoopDuration) /scaleLoopDuration;

        fXOffset = sinf(xLoopProgress * timeScale) * 0.5f;
        fYOffset = sinf(yLoopProgress * timeScale) * 0.5f;
        fZOffset = sinf(zLoopProgress * timeScale) * 0.5f;
        scale = 1/(1 + sinf(scaleLoopProgress * timeScale) * 0.5f);
}

void PrintMat4(float *mat)
{
        for(int i = 0; i < 4; i++)
        {
                for(int j = 0; j < 4; j++)
                {
                        std::cout << mat[j * 4 + i] << "\t";
                }
                std::cout << std::endl;
        }
        std::cout << std::endl;
}
4

3 回答 3

1

一些东西：

首先，您似乎将投影矩阵的“眼睛”设置为 [0, 0 -1]，将“相机”推向屏幕背面。如果是这种情况，您必须将对象移动到超出该点才能让它们出现是很正常的。

罪魁祸首是（我认为，你的变量名不是特别清楚:-/）：

a[3 + 4 * 2] = -1.0f;

我会尝试将其更改为

a[3 + 4 * 2] = 1.0f;

看看这是否有所作为。

其次，根据您要渲染的内容，您的“相机”可能恰好在您的网格内。由于您启用了背面剔除，因此您将看不到任何东西，因为所有可见的面都被剔除，并且将您的模型移得更远会将未剔除的面放在视野中。要查看这是否是问题，请更改行

glEnable(GL_CULL_FACE);

到

glDisable(GL_CULL_FACE);

看看你的“相机”是否在你的网格内。

第三，您的网格可能位于“相机”和近平面之间。尝试玩 zNear 看看它是否有所作为。zFar 可能是正确的，因为当您将它们移开时您的对象会出现。

编辑：所以我更详细地研究了它并试图找出你的投影矩阵。根据对透视投影背后数学的伟大解释，您的投影矩阵生成代码似乎正确地生成了一个向下看的矩阵 -Z。基本上，您的代码按预期工作，因为 OpenGL 默认使用右手坐标系。

如果您希望能够在 +Z 中偏移您的对象，因为负值会让您烦恼，您可以创建一个围绕 Y 轴执行 180 度旋转的视图矩阵，并将其与投影矩阵相乘。然后你会得到

finalCoordinates = projection * view * model * vertex;

TL；DR：您的代码按预期工作。

于 2013-07-02T14:19:36.120 回答
0

我没有检查您的代码，但这是一个简单的答案：由于 OpenGL 使用所谓的右手坐标系，负 z 值表示“进入”屏幕的方向，而正 z 值表示“离开屏幕” " （即用右手，拇指指向右边 -> 正 x 轴。你的第一根手指指向上方，与拇指成直角 -> 正 y 轴。最后但并非最不重要的一点：你的中指，右 -与你的第一根手指和你的重击成角度，指向你 -> 正 z 轴！）

于 2013-07-02T14:08:23.700 回答
0

我发现这个网站非常有用：

http://www.scratchapixel.com/lessons/3d-advanced-lessons/perspective-and-orthographic-projection-matrix/opengl-perspective-projection-matrix/

它很好地解释了您感兴趣的主题。

于 2013-07-06T16:58:42.093 回答