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//! Transformation utilities.
//!
//! Some space definitions to keep in mind:
//!
//! Texture coordinates:
//! * origin top left
//! * full texture ([left; right], [top; bottom]):
//! ([0; 1], [0; 1])
//!
//! NDC:
//! * origin center
//! * full screen ([left; right], [top; bottom]):
//! ([-1; 1], [1; -1])
//!
//! Pixel coordinates:
//! * origin top left
//! * full screen ([left; right], [top; bottom]):
//! ([0; `screen_extent.x`], [0; `screen_extent.y`])
use crate::rect::RectF32;
/// Transforms texture coordinates to normalized device coordinates (NDC).
#[inline]
pub fn ndc_from_texcoord(texcoord: glam::Vec2) -> glam::Vec2 {
glam::vec2(texcoord.x * 2.0 - 1.0, 1.0 - texcoord.y * 2.0)
}
/// Transforms texture coordinates to normalized device coordinates (NDC).
#[inline]
pub fn ndc_from_pixel(pixel_coord: glam::Vec2, screen_extent: glam::UVec2) -> glam::Vec2 {
glam::vec2(
pixel_coord.x / screen_extent.x as f32 * 2.0 - 1.0,
1.0 - pixel_coord.y / screen_extent.y as f32 * 2.0,
)
}
/// Defines a transformation from a rectangular region of interest into a rectangular target region.
///
/// This is "pan and scan".
///
/// Transforms the range of `region_of_interest` to the range of `region`.
#[derive(Clone, Debug)]
pub struct RectTransform {
/// The region of the scene that should be visible.
pub region_of_interest: RectF32,
/// The full scene.
pub region: RectF32,
}
impl RectTransform {
/// No-op rect transform that transforms from a unit rectangle to a unit rectangle.
pub const IDENTITY: Self = Self {
region_of_interest: RectF32::UNIT,
region: RectF32::UNIT,
};
/// Computes a transformation matrix that applies the rect transform to the NDC space.
///
/// This matrix is expected to be the left most transformation in the vertex transformation chain.
/// It causes the area described by `region_of_interest` to be mapped to the area described by `region`.
/// Meaning, that `region` represents the full screen of the NDC space.
///
/// This means that only the relation of the rectangles in `RectTransform` is important.
/// Scaling or moving both rectangles by the same amount does not change the result.
pub fn to_ndc_scale_and_translation(&self) -> glam::Mat4 {
// It's easier to think in texcoord space, and then transform to NDC.
// This texcoord rect specifies the portion of the screen that should become the entire range of the NDC screen.
let texcoord_rect = RectF32 {
min: (self.region_of_interest.min - self.region.min) / self.region.extent,
extent: self.region_of_interest.extent / self.region.extent,
};
let texcoord_rect_min = texcoord_rect.min;
let texcoord_rect_max = texcoord_rect.max();
// y axis is flipped in NDC, therefore we need to flip the y axis of the rect.
let rect_min_ndc = ndc_from_texcoord(glam::vec2(texcoord_rect_min.x, texcoord_rect_max.y));
let rect_max_ndc = ndc_from_texcoord(glam::vec2(texcoord_rect_max.x, texcoord_rect_min.y));
let scale = 2.0 / (rect_max_ndc - rect_min_ndc);
let translation = -0.5 * (rect_min_ndc + rect_max_ndc);
glam::Mat4::from_scale(scale.extend(1.0))
* glam::Mat4::from_translation(translation.extend(0.0))
}
pub fn scale(&self) -> glam::Vec2 {
self.region_of_interest.extent / self.region.extent
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
pub fn to_ndc_scale_and_translation() {
let region = RectF32 {
min: glam::vec2(1.0, 1.0),
extent: glam::vec2(2.0, 3.0),
};
// Identity
{
let rect_transform = RectTransform {
region_of_interest: region,
region,
};
let identity = rect_transform.to_ndc_scale_and_translation();
assert_eq!(identity, glam::Mat4::IDENTITY);
}
// Scale
{
let scale_factor = glam::vec2(2.0, 0.25);
let rect_transform = RectTransform {
region_of_interest: RectF32 {
// Move the roi to the middle of the region.
min: region.center() - region.extent * scale_factor * 0.5,
extent: region.extent * scale_factor,
},
region,
};
let scale = rect_transform.to_ndc_scale_and_translation();
assert_eq!(
scale,
glam::Mat4::from_scale(1.0 / scale_factor.extend(1.0))
);
assert_eq!(rect_transform.scale(), scale_factor);
}
// Translation
{
let translation_vec = glam::vec2(1.0, 2.0);
let rect_transform = RectTransform {
region_of_interest: RectF32 {
min: region.min + translation_vec * region.extent,
extent: region.extent,
},
region,
};
let translation = rect_transform.to_ndc_scale_and_translation();
assert_eq!(
translation,
glam::Mat4::from_translation(
glam::vec3(-translation_vec.x, translation_vec.y, 0.0) * 2.0
)
);
assert_eq!(rect_transform.scale(), glam::Vec2::ONE);
}
// Scale + translation
{
let scale_factor = glam::vec2(2.0, 0.25);
let translation_vec = glam::vec2(1.0, 2.0);
let rect_transform = RectTransform {
region_of_interest: RectF32 {
// Move the roi to the middle of the region and then apply translation
min: region.center() - region.extent * scale_factor * 0.5
+ translation_vec * region.extent,
extent: region.extent * scale_factor,
},
region,
};
let scale_and_translation = rect_transform.to_ndc_scale_and_translation();
assert_eq!(
scale_and_translation,
glam::Mat4::from_scale(1.0 / scale_factor.extend(1.0))
* glam::Mat4::from_translation(
glam::vec3(-translation_vec.x, translation_vec.y, 0.0) * 2.0
)
);
assert_eq!(rect_transform.scale(), scale_factor);
}
}
}