## The Model matrix

This model, just as our beloved red triangle, is defined by a set of vertices. The X,Y,Z coordinates of these vertices are defined relative to the object’s center : that is, if a vertex is at (0,0,0), it is at the center of the object.

We can sum this up with the following diagram :

## The View matrix

We went from World Space (all vertices defined relatively to the center of the world, as we made so in the previous section) to Camera Space (all vertices defined relatively to the camera).

Here’s the compulsory diagram :

## The Projection matrix

We’re now in Camera Space. This means that after all theses transformations, a vertex that happens to have x==0 and y==0 should be rendered at the center of the screen.

And the final diagram :

### Parallelepiped

void Parallelepiped::init()
{
glm::vec3 pu = p + u;
glm::vec3 pv = p + v;
glm::vec3 pw = p + w;
glm::vec3 puv = p + u + v;
glm::vec3 pvw = p + v + w;
glm::vec3 puw = p + u + w;
glm::vec3 puvw = p + u + v + w;

// Front face
vbo.addData(&p[0], sizeof(glm::vec3));
vbo.addData(&pu[0], sizeof(glm::vec3));
vbo.addData(&puw[0], sizeof(glm::vec3));
vbo.addData(&p[0], sizeof(glm::vec3));
vbo.addData(&puw[0], sizeof(glm::vec3));
vbo.addData(&pw[0], sizeof(glm::vec3));

// Back face
vbo.addData(&puv[0], sizeof(glm::vec3));
vbo.addData(&pv[0], sizeof(glm::vec3));
vbo.addData(&pvw[0], sizeof(glm::vec3));
vbo.addData(&puv[0], sizeof(glm::vec3));
vbo.addData(&pvw[0], sizeof(glm::vec3));
vbo.addData(&puvw[0], sizeof(glm::vec3));

// Left face
vbo.addData(&pv[0], sizeof(glm::vec3));
vbo.addData(&p[0], sizeof(glm::vec3));
vbo.addData(&pw[0], sizeof(glm::vec3));
vbo.addData(&pv[0], sizeof(glm::vec3));
vbo.addData(&pw[0], sizeof(glm::vec3));
vbo.addData(&pvw[0], sizeof(glm::vec3));

// Right face
vbo.addData(&pu[0], sizeof(glm::vec3));
vbo.addData(&puv[0], sizeof(glm::vec3));
vbo.addData(&puvw[0], sizeof(glm::vec3));
vbo.addData(&pu[0], sizeof(glm::vec3));
vbo.addData(&puvw[0], sizeof(glm::vec3));
vbo.addData(&puw[0], sizeof(glm::vec3));

// Top face
vbo.addData(&pw[0], sizeof(glm::vec3));
vbo.addData(&puw[0], sizeof(glm::vec3));
vbo.addData(&puvw[0], sizeof(glm::vec3));
vbo.addData(&pw[0], sizeof(glm::vec3));
vbo.addData(&puvw[0], sizeof(glm::vec3));
vbo.addData(&pvw[0], sizeof(glm::vec3));

// Bottom face
vbo.addData(&puv[0], sizeof(glm::vec3));
vbo.addData(&pu[0], sizeof(glm::vec3));
vbo.addData(&p[0], sizeof(glm::vec3));
vbo.addData(&puv[0], sizeof(glm::vec3));
vbo.addData(&p[0], sizeof(glm::vec3));
vbo.addData(&pv[0], sizeof(glm::vec3));

numVertices = 36;

// create VBO
vbo.createVBO();
vbo.bindVBO();
vbo.uploadDataToGPU(GL_STATIC_DRAW);

// create a VAO
glGenVertexArrays(1, &vao);
glBindVertexArray(vao);
glEnableVertexAttribArray(0);
glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 0, 0);

isLoaded = true;
}

### Quad

void Quad::init()
{
glm::vec3 left = glm::cross(n, u);
glm::vec3 uppercenter = (u * height/2.0f) + p;
glm::vec3 tl = uppercenter + (left * width/2.0f);
glm::vec3 tr = uppercenter – (left * width/2.0f);
glm::vec3 bl = tl – (u * height);
glm::vec3 br = tr – (u * height);

// face 1
vbo.addData(&bl[0], sizeof(glm::vec3)); // vertex position
vbo.addData(&color[0], sizeof(glm::vec3)); // vertex color
vbo.addData(&br[0], sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3));
vbo.addData(&tr[0], sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3));

// face 2
vbo.addData(&bl[0], sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3));
vbo.addData(&tr[0], sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3));
vbo.addData(&tl[0], sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3));

numVertices = 6;

// VAO & VBOs
vbo.createVBO();
vbo.bindVBO();
vbo.uploadDataToGPU(GL_STATIC_DRAW);

glGenVertexArrays(1, &vao);
glBindVertexArray(vao);

int iDataStride = 2 * sizeof(glm::vec3); // vertex & color only
int iDataOffset = 0;
glEnableVertexAttribArray(0);
glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, iDataStride, (void*)iDataOffset);
iDataOffset += sizeof(glm::vec3);
glEnableVertexAttribArray(1);
glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, iDataStride, (void*)iDataOffset);

isLoaded = true;
}

### Triangle

void Triangle::init()
{
glm::vec3 t1 = p + v1;
glm::vec3 t2 = p + v2;
glm::vec3 t3 = p + v3;

// face 1
vbo.addData(&t1[0], sizeof(glm::vec3)); // vertex position
vbo.addData(&color[0], sizeof(glm::vec3)); // vertex color
vbo.addData(&t2[0], sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3));
vbo.addData(&t3[0], sizeof(glm::vec3));
vbo.addData(&color[0], sizeof(glm::vec3));

numVertices = 3;

// VAO & VBOs
vbo.createVBO();
vbo.bindVBO();
vbo.uploadDataToGPU(GL_STATIC_DRAW);

glGenVertexArrays(1, &vao);
glBindVertexArray(vao);

int iDataStride = 2 * sizeof(glm::vec3); // vertex & color only
int iDataOffset = 0;
glEnableVertexAttribArray(0);
glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, iDataStride, (void*)iDataOffset);
iDataOffset += sizeof(glm::vec3);
glEnableVertexAttribArray(1);
glVertexAttribPointer(1, 3, GL_FLOAT, GL_FALSE, iDataStride, (void*)iDataOffset);

isLoaded = true;
}

### Project Idea Presentation

Project Idea Presentation (9/27) 프로젝트 제목, 내용, HW/SW
1. 김철민, 홍석영, 유인혁 – Four Seasons (Unity3D 사용) 산사의 사계절을 표현
2. 강준구, 박희찬, 장유곤 – first-person narrative 3D graphics viewer (비트코인 시세를 3D 가시화) Modern OpenGL 사용
3. 김재윤, 김태현, 김은채 – 리듬 게임 (Unity3D)
4. 이영석, 김건우 – 갤로그 슈팅 게임 (Unity3D/OpenGL)

### lab2

Lab2-GeometryPositionColor (using Model-View-Projection matrix)

lab2-moglclassGeometryPositionColor

Geometry – Triangle, Quad, Circle, Sphere, Cube, Cylinder, Torus, Parallelpiped

int main( int argc, char **argv )
{
glutInit(&argc, argv);
glutInitDisplayMode( GLUT_SINGLE | GLUT_RGBA | GLUT_DEPTH );

}

void init( void )
{

glEnable(GL_DEPTH_TEST); // enable depth test
glClearColor( 1.0, 1.0, 1.0, 1.0 ); // white background
}

void display( void )
{
glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT ); // clear the window

glFlush();

}

// using Uniform variables to shader
float g_fovy = 45.0f;
float g_aspect = 1.0f;
float g_zNear = 1.0f;
float g_zFar = 100.f;

glm::vec3 g_eye(0, 0, 3.0f);
glm::vec3 g_at(0, 0, 0);
glm::vec3 g_up(0, 1, 0);

// Model View Projection matrix
glm::mat4 World(1.0f);
glm::mat4 View(1.0f);
glm::mat4 Projection(1.0f);
glm::mat4 MVP(1.0f);

void display( void )
{
glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT ); // clear the window

// set drawmode
if (g_wiremode)
glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);  // draw wireframe
else
glPolygonMode(GL_FRONT_AND_BACK, GL_FILL); // draw filled

// Model-View-Projection matrix
Projection = glm::perspective(g_fovy, g_aspect, g_zNear, g_zFar);
View = glm::lookAt(g_eye, g_at, g_up);
World = yRotation;
MVP = Projection * View * World;
spMain.useProgram();
spMain.setUniform(“gMVP“, MVP);

}

void reshape(int w, int h)
{
g_aspect = (float) (w/h);
glViewport(0, 0, (GLsizei) w, (GLsizei) h);
glutPostRedisplay();
}

void specialkey(int key, int x, int y)
{
switch (key) {
case GLUT_KEY_UP:
g_eye.z += 2;
break;
case GLUT_KEY_DOWN:
g_eye.z -= 2;
break;
case GLUT_KEY_LEFT:
g_at.x -= 1;
g_eye.x -= 1;
break;
case GLUT_KEY_RIGHT:
g_at.x += 1;
g_eye.x += 1;
break;
}
glutPostRedisplay();
}

//////////////////////////////////////////////

simple3.vs

//////////////////////////////////////////////

uniform mat4 gMVP;

in vec3 vPosition;
in vec3 inColor;
out vec4 Color;

void
main()
{
gl_Position = gMVP * vec4(vPosition, 1);
Color = vec4(inColor, 1);
}