Return to Answer

completely misunderstood the question, edited it to make it better

Source Link

edited Jul 23, 2010 at 9:36

5.6k
1
27
31

EDIT: What the hell, I completely misinterpreted the question! Saved for posterity (I thought the question was "how do I get an object to spin around another object):

What you need to learn about is something called a scene graph. The basic principle is very simple:

I hope this answers your question. :)

EDIT: After you've done this, you now have both the object and the camera in world space. The main thing about rasterization is that you have to transform the world coordinates into screen coordinates somehow.

The easiest way to do this is to ignore z:

screen.x = world.x;
screen.y = world.y;

If you have a rotating teapot, you will see a rotating teapot on the screen. However this isn't a very good implementation. If you want to do it correctly, you will have to subtract from the world position the camera position (effectively turning world space positions into camera space positions) and use the camera matrix to transform the coordinates.

Here's how I project a triangle in my own software rasterizer:

Vec3 camera_space;

for (int i = 0; i < 3; i++)
{
    Vec3 translated = a_Triangle->v[i] - m_Position;
    
    camera_space.x = 
        (translated.x * m_Rotation[Mat4x4::X1]) + 
        (translated.y * m_Rotation[Mat4x4::Y1]) + 
        (translated.z * m_Rotation[Mat4x4::Z1]);

    camera_space.y = 
        (translated.x * m_Rotation[Mat4x4::X2]) + 
        (translated.y * m_Rotation[Mat4x4::Y2]) + 
        (translated.z * m_Rotation[Mat4x4::Z2]);

    camera_space.z = 
        (translated.x * m_Rotation[Mat4x4::X3]) + 
        (translated.y * m_Rotation[Mat4x4::Y3]) + 
        (translated.z * m_Rotation[Mat4x4::Z3]);

    //#define FOV_ANGLE                 60.f
    //static const float FOV_TAN      = tanf(Math::RadToDeg(FOV_ANGLE) / 2);
    const float distance = m_TargetHeightHalf / (FOV_TAN * camera_space.z);

    a_Triangle->p[i].x = m_TargetWidthHalf  + (camera_space.x *  distance);
    a_Triangle->p[i].y = m_TargetHeightHalf + (camera_space.y * -distance);
    a_Triangle->depth[i] = -distance;
}

What you need to learn about is something called a scene graph. The basic principle is very simple:

I hope this answers your question. :)

EDIT: What the hell, I completely misinterpreted the question! Saved for posterity (I thought the question was "how do I get an object to spin around another object):

What you need to learn about is something called a scene graph. The basic principle is very simple:

I hope this answers your question. :)

The easiest way to do this is to ignore z:

screen.x = world.x;
screen.y = world.y;

Here's how I project a triangle in my own software rasterizer:

Vec3 camera_space;

for (int i = 0; i < 3; i++)
{
    Vec3 translated = a_Triangle->v[i] - m_Position;
    
    camera_space.x = 
        (translated.x * m_Rotation[Mat4x4::X1]) + 
        (translated.y * m_Rotation[Mat4x4::Y1]) + 
        (translated.z * m_Rotation[Mat4x4::Z1]);

    camera_space.y = 
        (translated.x * m_Rotation[Mat4x4::X2]) + 
        (translated.y * m_Rotation[Mat4x4::Y2]) + 
        (translated.z * m_Rotation[Mat4x4::Z2]);

    camera_space.z = 
        (translated.x * m_Rotation[Mat4x4::X3]) + 
        (translated.y * m_Rotation[Mat4x4::Y3]) + 
        (translated.z * m_Rotation[Mat4x4::Z3]);

    //#define FOV_ANGLE                 60.f
    //static const float FOV_TAN      = tanf(Math::RadToDeg(FOV_ANGLE) / 2);
    const float distance = m_TargetHeightHalf / (FOV_TAN * camera_space.z);

    a_Triangle->p[i].x = m_TargetWidthHalf  + (camera_space.x *  distance);
    a_Triangle->p[i].y = m_TargetHeightHalf + (camera_space.y * -distance);
    a_Triangle->depth[i] = -distance;
}

Source Link

answered Jul 23, 2010 at 9:08

knight666

5.6k
1
27
31

What you need to learn about is something called a scene graph. The basic principle is very simple:

Suppose you have a 2D field. You have an X-axis and a Y-axis. Define a cube with four coordinates:

alt text

Now we rotate it 45 degrees. The blue box is the result:

alt text

Now we translate it to the left and up:

alt text

Let's do this in reverse. First we translate and then we rotate:

alt text

The result is completely different!

What you want to do in a scene graph is multiply a node's matrix with its parent. You want to translate the coordinates of a node from local space (hand) to world space (hand -> arm -> body -> world).

Effectively, you want to have a top node (your root node) with a bunch of children. When you want to render, you start at the top node and tell its children to render with the top matrix:

void SceneNode::Render(Mat4x4* a_Matrix)
{
    Mat4x4 final = a_Matrix * m_Matrix;

    if (m_Model) 
    { 
        m_Model->Render(final);
    }

    if (m_Children.size() > 0)
    {
        for (std::vector<SceneNode*>::iterator i = m_Children.begin(); i != m_Children.end(); ++i)
        {
            (*i)->Render(&final);
        }
    }
}

I hope this answers your question. :)