PixSpace/src/projection.rs

use bevy::prelude::*;
use bevy::math::{Mat4, Quat, Affine3A};

/// creates a conventional projection matrix from frustum planes
/// 
/// returns a potentially off-axis projection matrix
pub fn make_projection_rh_from_frustum(left: f32, right: f32, bottom: f32, top: f32, near:f32, far:f32) -> Mat4
{
    // based on OpenSceneGraph / glFrustum implementation
    let a = (right + left) / (right - left);
    let b: f32 = (top + bottom) / (top - bottom);
    let c= if far.abs() > f32::MAX  { -1.0 } else { -(far + near) / (far - near)};
    let d = if far.abs() > f32::MAX { -2.0 * near } else { -2.0 * far * near / (far - near) };

    Mat4::from_cols( 
        Vec4::new(2.0 * near / (right-left),0.0,0.0,0.0), 
        Vec4::new(0.0, 2.0 *near / (top-bottom), 0.0,0.0),
        Vec4::new(a, b, c, -1.0),
        Vec4::new(0.0, 0.0, d, 0.0))
}

/// creates a projection from a frustum planes with a reversed depth mapped to [0..1]
pub fn make_projection_rh_from_frustum_reversed(left: f32, right: f32, bottom: f32, top: f32, z_near:f32, z_far:f32) -> Mat4
{
    assert!(z_near > 0.0 && z_far > 0.0);

    //
    // reversed z 0..1 projection based on https://thxforthefish.com/posts/reverse_z/
    //
    let a = (right + left) / (right - left);
    let b = (top + bottom) / (top - bottom);
    
    let c =  z_near / (z_far - z_near);
    let d =  z_far * z_near / (z_far - z_near);


    Mat4::from_cols( 
        Vec4::new(2.0 * z_near / (right-left),        0.0,0.0,0.0),
        Vec4::new(0.0, 2.0 * z_near / (top-bottom),   0.0,0.0),
        Vec4::new(a, b, c, -1.0),
        Vec4::new(0.0, 0.0, d, 0.0))
}


pub fn make_projection_rh_custom(fov_y: f32, aspect_ratio: f32, z_near: f32, z_far: f32) -> Mat4
{
    let tan_fovy = (fov_y * 0.5).tan(); // use half angle beta
    let right = tan_fovy * aspect_ratio * z_near;
    let left = -right;
    let top = tan_fovy * z_near;
    let bottom = -top;

    //make_projection_rh_from_frustum(left, right, bottom, top, z_near, z_far)

    make_projection_rh_from_frustum_reversed(left, right, bottom, top, z_near, z_far)
}


pub fn create_offaxis_matrices(
    screen_lower_left: Vec3,
    screen_lower_right: Vec3,
    screen_upper_left: Vec3,
    pos_eye: Vec3,
    z_far: f32
    ) -> (Mat4,Mat4)
{

    // 
    let vec_right = screen_lower_right - screen_lower_left; // vr
    let vec_up = screen_upper_left - screen_lower_left;     // vu
    
    let frustum_left = screen_lower_left - pos_eye;     // va
    let frustum_right = screen_lower_right - pos_eye;   // vb
    let frustum_up = screen_upper_left - pos_eye;       // vc

    let vec_right_normalized = vec_right.normalize();
    let vec_up_normalized = vec_up.normalize();

    let vec_normal = vec_right_normalized.cross(vec_up_normalized).normalize();

    let dist = -frustum_left.normalize().dot(vec_normal);

    // println!("vec_right_normalized {}",vec_right_normalized);
    // println!("vec_up_normalized {}",vec_up_normalized);
    // println!("vec_normal {}",vec_normal);

    // println!("Dist {}",dist);

    // small offset for the near plane 
    let min_near_distance_offset = 0.01f32;

    // set a minimal near distance
    let min_near_distance = 0.00001f32;

    // calculate a reasonable near distance
    let z_near = min_near_distance.max(dist - min_near_distance_offset);

    // distances 
    let left = vec_right_normalized.dot(frustum_left) * z_near / dist;  // left screen edge
    let right = vec_right_normalized.dot(frustum_right) * z_near / dist;    // right screen edge
    let bottom = vec_up_normalized.dot(frustum_left) * z_near / dist;   // bottom screen edge
    let top = vec_up_normalized.dot(frustum_up) * z_near / dist;    // distance eye from screen

    // info!("l r b t {} {} {} {}",left,right,bottom,top);

    // create a view frustum
    let projection_matrix = make_projection_rh_from_frustum_reversed(left,right,bottom,top,z_near,z_far);

    let view_matrix_rotation = Mat4::from_cols(
        Vec4::new(vec_right_normalized.x, vec_up_normalized.x, vec_normal.x  ,0.0),
        Vec4::new(vec_right_normalized.y, vec_up_normalized.y, vec_normal.y  ,0.0),
        Vec4::new(vec_right_normalized.z, vec_up_normalized.z, vec_normal.z  ,0.0),
        Vec4::W
    );

    let rotation_quat = Quat::from_mat4(&view_matrix_rotation); // Quat::from_mat4(view_matrix_rotation);

    // info!("Rotation Mat {:?}",view_matrix_rotation);
    // info!("Viewer Rotation {:?}",rotation_quat);

    let view_matrix_eye = Mat4::from_cols(
        Vec4::X,
        Vec4::Y,
        Vec4::Z,
        (-pos_eye).extend(1.0)        
    );

    // create resulting view matrix (this should be much simpler using glam API)
    let view_matrix = view_matrix_rotation * view_matrix_eye;

    // return tuple of view and projection
    (view_matrix,projection_matrix)
}



#[cfg(test)]
mod tests {
    use bevy::prelude::*;

    use crate::{screeninfo, projection::create_offaxis_matrices};

    use super::make_projection_rh_from_frustum;


    #[test]
    fn compare_projections() {

        // build an on-axis frustum
        let fovy = 33.0_f32;
        let aspect_ratio = 1.6666_f32;
        let z_near = 1.0_f32;
        let z_far = 1000.0_f32;

        let tan_fovy = (fovy * 0.5).to_radians().tan(); // use half angle beta
        let right = tan_fovy * aspect_ratio * z_near;
        let left = -right;
        let top = tan_fovy * z_near;
        let bottom = -top;

        let mat_frust = make_projection_rh_from_frustum(left, right, bottom, top, z_near, z_far);

        println!("mat 1 {:?}",mat_frust);

        let mat_pers = Mat4::perspective_rh_gl(fovy.to_radians(),aspect_ratio,z_near,z_far);

        println!("mat 2 {:?}",mat_pers);

        assert!(mat_frust.abs_diff_eq(mat_pers, f32::EPSILON));

    }


    #[test]
    fn create_view_matrices() {

        // Assumptions: Screensize 6.0m x 1.8m 
        // Viewer is 5m away from center


        let screen_lower_left = Vec3::new(-3.0,-0.9,0.0);
        let screen_lower_right = Vec3::new(3.0,-0.9,0.0);
        let screen_upper_left = Vec3::new(-3.0,0.9,0.0);


        let eye_pos = Vec3::Z * 5.0;

        let z_far = 100.0_f32;

        
        let (view,projection) = create_offaxis_matrices(screen_lower_left, screen_lower_right, screen_upper_left, eye_pos, z_far);


        println!("View {:?}",view);
        println!("Projection {:?}",projection);

        // assert!(!view.is_nan());
        // assert!(!projection.is_nan());
    
    }

}