# Concept

We analyze the object:

• Minimum coordinates in X, Y and Z
• Maximum coordinates in X, Y and Z
• We compute the size necessary for the object: `max-min` in X, Y and Z
• We compute the center of the object: `(min+max)/2` in X, Y and Z

We compute of cube around the object:

• We prepare a cube of size 1 (1x1x1), centered on the origin
• We scale it by the size of the object
• We center it on the object

To draw the cube:

• We draw the front face using 1 looping line
• We draw the back face using 1 looping line
• We draw 4 orthogonal lines to join both faces

# Code

```void draw_bbox(struct mesh* mesh) {
if (mesh->vertices.size() == 0)
return;

// Cube 1x1x1, centered on origin
GLfloat vertices[] = {
-0.5, -0.5, -0.5, 1.0,
0.5, -0.5, -0.5, 1.0,
0.5,  0.5, -0.5, 1.0,
-0.5,  0.5, -0.5, 1.0,
-0.5, -0.5,  0.5, 1.0,
0.5, -0.5,  0.5, 1.0,
0.5,  0.5,  0.5, 1.0,
-0.5,  0.5,  0.5, 1.0,
};
GLuint vbo_vertices;
glGenBuffers(1, &vbo_vertices);
glBindBuffer(GL_ARRAY_BUFFER, vbo_vertices);
glBufferData(GL_ARRAY_BUFFER, sizeof(vertices), vertices, GL_STATIC_DRAW);
glBindBuffer(GL_ARRAY_BUFFER, 0);

GLushort elements[] = {
0, 1, 2, 3,
4, 5, 6, 7,
0, 4, 1, 5, 2, 6, 3, 7
};
GLuint ibo_elements;
glGenBuffers(1, &ibo_elements);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ibo_elements);
glBufferData(GL_ELEMENT_ARRAY_BUFFER, sizeof(elements), elements, GL_STATIC_DRAW);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, 0);

GLfloat
min_x, max_x,
min_y, max_y,
min_z, max_z;
min_x = max_x = mesh->vertices.x;
min_y = max_y = mesh->vertices.y;
min_z = max_z = mesh->vertices.z;
for (int i = 0; i < mesh->vertices.size(); i++) {
if (mesh->vertices[i].x < min_x) min_x = mesh->vertices[i].x;
if (mesh->vertices[i].x > max_x) max_x = mesh->vertices[i].x;
if (mesh->vertices[i].y < min_y) min_y = mesh->vertices[i].y;
if (mesh->vertices[i].y > max_y) max_y = mesh->vertices[i].y;
if (mesh->vertices[i].z < min_z) min_z = mesh->vertices[i].z;
if (mesh->vertices[i].z > max_z) max_z = mesh->vertices[i].z;
}
glm::vec3 size = glm::vec3(max_x-min_x, max_y-min_y, max_z-min_z);
glm::vec3 center = glm::vec3((min_x+max_x)/2, (min_y+max_y)/2, (min_z+max_z)/2);
glm::mat4 transform = glm::translate(glm::mat4(1), center) * glm::scale(glm::mat4(1), size);

/* Apply object's transformation matrix */
glm::mat4 m = mesh->object2world * transform;
glUniformMatrix4fv(uniform_m, 1, GL_FALSE, glm::value_ptr(m));

glBindBuffer(GL_ARRAY_BUFFER, vbo_vertices);
glEnableVertexAttribArray(attribute_v_coord);
glVertexAttribPointer(
attribute_v_coord,  // attribute
4,                  // number of elements per vertex, here (x,y,z,w)
GL_FLOAT,           // the type of each element
GL_FALSE,           // take our values as-is
0,                  // no extra data between each position
0                   // offset of first element
);

glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ibo_elements);
glDrawElements(GL_LINE_LOOP, 4, GL_UNSIGNED_SHORT, 0);
glDrawElements(GL_LINE_LOOP, 4, GL_UNSIGNED_SHORT, (GLvoid*)(4*sizeof(GLushort)));
glDrawElements(GL_LINES, 8, GL_UNSIGNED_SHORT, (GLvoid*)(8*sizeof(GLushort)));
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, 0);

glDisableVertexAttribArray(attribute_v_coord);
glBindBuffer(GL_ARRAY_BUFFER, 0);

glDeleteBuffers(1, &vbo_vertices);
glDeleteBuffers(1, &ibo_elements);
}
```

# Intersection with surfaces

As seen in Scientific tutorial 05, you can improve situations where lines and surfaces are mixing, by using:

```/* main */
glEnable(GL_POLYGON_OFFSET_FILL);
glPolygonOffset(1, 0);
```

Keep `GL_POLYGON_OFFSET_FILL` enabled even after you draw the lines, it needs to be enabled when drawing the surfaces as well.

You can also increase the line thickness if need be:

```    glLineWidth(2);
```