sparse_strips/vello_common/src/strip.rs

// Copyright 2025 the Vello Authors
// SPDX-License-Identifier: Apache-2.0 OR MIT

//! Rendering strips.

use alloc::vec::Vec;
use vello_api::peniko::Fill;

use crate::flatten::Line;
use crate::tile::{Tile, Tiles};

/// A strip.
#[derive(Debug, Clone, Copy)]
pub struct Strip {
    /// The x coordinate of the strip, in user coordinates.
    pub x: u16,
    /// The y coordinate of the strip, in user coordinates.
    pub y: u16,
    /// The index into the alpha buffer.
    pub alpha_idx: u32,
    /// The winding number at the start of the strip.
    pub winding: i32,
}

impl Strip {
    /// Return the y coordinate of the strip, in strip units.
    pub fn strip_y(&self) -> u16 {
        self.y / Tile::HEIGHT
    }
}

/// Render the tiles stored in `tiles` into the strip and alpha buffer.
/// The strip buffer will be cleared in the beginning.
pub fn render(
    tiles: &Tiles,
    strip_buf: &mut Vec<Strip>,
    alpha_buf: &mut Vec<u8>,
    fill_rule: Fill,
    lines: &[Line],
) {
    strip_buf.clear();

    if tiles.is_empty() {
        return;
    }

    // The accumulated tile winding delta. A line that crosses the top edge of a tile
    // increments the delta if the line is directed upwards, and decrements it if goes
    // downwards. Horizontal lines leave it unchanged.
    let mut winding_delta: i32 = 0;

    // The previous tile visited.
    let mut prev_tile = *tiles.get(0);
    // The accumulated (fractional) winding of the tile-sized location we're currently at.
    // Note multiple tiles can be at the same location.
    let mut location_winding = [[0_f32; Tile::HEIGHT as usize]; Tile::WIDTH as usize];
    // The accumulated (fractional) windings at this location's right edge. When we move to the
    // next location, this is splatted to that location's starting winding.
    let mut accumulated_winding = [0_f32; Tile::HEIGHT as usize];

    /// A special tile to keep the logic below simple.
    const SENTINEL: Tile = Tile::new(u16::MAX, u16::MAX, 0, false);

    // The strip we're building.
    let mut strip = Strip {
        x: prev_tile.x * Tile::WIDTH,
        y: prev_tile.y * Tile::HEIGHT,
        alpha_idx: alpha_buf.len() as u32,
        winding: 0,
    };

    for (tile_idx, tile) in tiles.iter().copied().chain([SENTINEL]).enumerate() {
        let line = lines[tile.line_idx() as usize];
        let tile_left_x = f32::from(tile.x) * f32::from(Tile::WIDTH);
        let tile_top_y = f32::from(tile.y) * f32::from(Tile::HEIGHT);
        let p0_x = line.p0.x - tile_left_x;
        let p0_y = line.p0.y - tile_top_y;
        let p1_x = line.p1.x - tile_left_x;
        let p1_y = line.p1.y - tile_top_y;

        // Push out the winding as an alpha mask when we move to the next location (i.e., a tile
        // without the same location).
        if !prev_tile.same_loc(&tile) {
            macro_rules! fill {
                ($rule:expr) => {
                    for x in 0..Tile::WIDTH as usize {
                        for y in 0..Tile::HEIGHT as usize {
                            let area = location_winding[x][y];
                            let coverage = $rule(area);
                            alpha_buf.push((coverage * 255.0 + 0.5) as u8);
                        }
                    }
                };
            }
            match fill_rule {
                Fill::NonZero => {
                    fill!(|area: f32| area.abs())
                }
                Fill::EvenOdd => {
                    // As in other parts of the code, we avoid using `round` since it's very
                    // slow on x86.
                    fill!(|area: f32| (area - 2.0 * ((0.5 * area) + 0.5).floor()).abs())
                }
            };

            #[expect(clippy::needless_range_loop, reason = "dimension clarity")]
            for x in 0..Tile::WIDTH as usize {
                location_winding[x] = accumulated_winding;
            }
        }

        // Push out the strip if we're moving to a next strip.
        if !prev_tile.same_loc(&tile) && !prev_tile.prev_loc(&tile) {
            debug_assert_eq!(
                (prev_tile.x + 1) * Tile::WIDTH - strip.x,
                ((alpha_buf.len() - strip.alpha_idx as usize) / usize::from(Tile::HEIGHT)) as u16,
                "The number of columns written to the alpha buffer should equal the number of columns spanned by this strip."
            );
            strip_buf.push(strip);

            let is_sentinel = tile_idx == tiles.len() as usize;
            if !prev_tile.same_row(&tile) {
                // Emit a final strip in the row if there is non-zero winding for the sparse fill,
                // or unconditionally if we've reached the sentinel tile to end the path (the
                // `alpha_idx` field is used for width calculations).
                if winding_delta != 0 || is_sentinel {
                    strip_buf.push(Strip {
                        x: u16::MAX,
                        y: prev_tile.y * Tile::HEIGHT,
                        alpha_idx: alpha_buf.len() as u32,
                        winding: winding_delta,
                    });
                }

                winding_delta = 0;
                accumulated_winding.fill(0.);

                #[expect(clippy::needless_range_loop, reason = "dimension clarity")]
                for x in 0..Tile::WIDTH as usize {
                    location_winding[x].fill(0.);
                }
            }

            if is_sentinel {
                break;
            }

            strip = Strip {
                x: tile.x * Tile::WIDTH,
                y: tile.y * Tile::HEIGHT,
                alpha_idx: alpha_buf.len() as u32,
                winding: winding_delta,
            };
            // Note: this fill is mathematically not necessary. It provides a way to reduce
            // accumulation of float rounding errors.
            accumulated_winding.fill(winding_delta as f32);
        }
        prev_tile = tile;

        // TODO: horizontal geometry has no impact on winding. This branch will be removed when
        // horizontal geometry is culled at the tile-generation stage.
        if p0_y == p1_y {
            continue;
        }

        // Lines moving upwards (in a y-down coordinate system) add to winding; lines moving
        // downwards subtract from winding.
        let sign = (p0_y - p1_y).signum();

        // Calculate winding / pixel area coverage.
        //
        // Conceptually, horizontal rays are shot from left to right. Every time the ray crosses a
        // line that is directed upwards (decreasing `y`), the winding is incremented. Every time
        // the ray crosses a line moving downwards (increasing `y`), the winding is decremented.
        // The fractional area coverage of a pixel is the integral of the winding within it.
        //
        // Practically, to calculate this, each pixel is considered individually, and we determine
        // whether the line moves through this pixel. The line's y-delta within this pixel is
        // accumulated and added to the area coverage of pixels to the right. Within the pixel
        // itself, the area to the right of the line segment forms a trapezoid (or a triangle in
        // the degenerate case). The area of this trapezoid is added to the pixel's area coverage.
        //
        // For example, consider the following pixel square, with a line indicated by asterisks
        // starting inside the pixel and crossing its bottom edge. The area covered is the
        // trapezoid on the bottom-right enclosed by the line and the pixel square. The area is
        // positive if the line moves down, and negative otherwise.
        //
        //  __________________
        //  |                |
        //  |         *------|
        //  |        *       |
        //  |       *        |
        //  |      *         |
        //  |     *          |
        //  |    *           |
        //  |___*____________|
        //     *
        //    *

        let (line_top_y, line_top_x, line_bottom_y, line_bottom_x) = if p0_y < p1_y {
            (p0_y, p0_x, p1_y, p1_x)
        } else {
            (p1_y, p1_x, p0_y, p0_x)
        };

        let (line_left_x, line_left_y, line_right_x) = if p0_x < p1_x {
            (p0_x, p0_y, p1_x)
        } else {
            (p1_x, p1_y, p0_x)
        };

        let y_slope = (line_bottom_y - line_top_y) / (line_bottom_x - line_top_x);
        let x_slope = 1. / y_slope;

        winding_delta += sign as i32 * i32::from(tile.winding());

        // TODO: this should be removed when out-of-viewport tiles are culled at the
        // tile-generation stage. That requires calculating and forwarding winding to strip
        // generation.
        if tile.x == 0 && line_left_x < 0. {
            let (ymin, ymax) = if line.p0.x == line.p1.x {
                (line_top_y, line_bottom_y)
            } else {
                let line_viewport_left_y = (line_top_y - line_top_x * y_slope)
                    .max(line_top_y)
                    .min(line_bottom_y);

                (
                    f32::min(line_left_y, line_viewport_left_y),
                    f32::max(line_left_y, line_viewport_left_y),
                )
            };

            for y_idx in 0..Tile::HEIGHT {
                let px_top_y = f32::from(y_idx);
                let px_bottom_y = 1. + f32::from(y_idx);

                let ymin = f32::max(ymin, px_top_y);
                let ymax = f32::min(ymax, px_bottom_y);

                let h = (ymax - ymin).max(0.);
                accumulated_winding[y_idx as usize] += sign * h;

                for x_idx in 0..Tile::WIDTH {
                    location_winding[x_idx as usize][y_idx as usize] += sign * h;
                }
            }

            if line_right_x < 0. {
                // Early exit, as no part of the line is inside the tile.
                continue;
            }
        }

        for y_idx in 0..Tile::HEIGHT {
            let px_top_y = f32::from(y_idx);
            let px_bottom_y = 1. + f32::from(y_idx);

            let ymin = f32::max(line_top_y, px_top_y);
            let ymax = f32::min(line_bottom_y, px_bottom_y);

            let mut acc = 0.;
            for x_idx in 0..Tile::WIDTH {
                let px_left_x = f32::from(x_idx);
                let px_right_x = 1. + f32::from(x_idx);

                // The y-coordinate of the intersections between the line and the pixel's left and
                // right edges respectively.
                //
                // There is some subtlety going on here: `y_slope` will usually be finite, but will
                // be `inf` for purely vertical lines (`p0_x == p1_x`).
                //
                // In the case of `inf`, the resulting slope calculation will be `-inf` or `inf`
                // depending on whether the pixel edge is left or right of the line, respectively
                // (from the viewport's coordinate system perspective). The `min` and `max`
                // y-clamping logic generalizes nicely, as a pixel edge to the left of the line is
                // clamped to `ymin`, and a pixel edge to the right is clamped to `ymax`.
                //
                // In the special case where a vertical line and pixel edge are at the exact same
                // x-position (collinear), the line belongs to the pixel on whose _left_ edge it is
                // situated. The resulting slope calculation for the edge the line is situated on
                // will be NaN, as `0 * inf` results in NaN. This is true for both the left and
                // right edge. In both cases, the call to `f32::max` will set this to `ymin`.
                let line_px_left_y = (line_top_y + (px_left_x - line_top_x) * y_slope)
                    .max(ymin)
                    .min(ymax);
                let line_px_right_y = (line_top_y + (px_right_x - line_top_x) * y_slope)
                    .max(ymin)
                    .min(ymax);

                // `x_slope` is always finite, as horizontal geometry is elided.
                let line_px_left_yx = line_top_x + (line_px_left_y - line_top_y) * x_slope;
                let line_px_right_yx = line_top_x + (line_px_right_y - line_top_y) * x_slope;
                let h = (line_px_right_y - line_px_left_y).abs();

                // The trapezoidal area enclosed between the line and the right edge of the pixel
                // square.
                let area = 0.5 * h * (2. * px_right_x - line_px_right_yx - line_px_left_yx);
                location_winding[x_idx as usize][y_idx as usize] += acc + sign * area;
                acc += sign * h;
            }
            accumulated_winding[y_idx as usize] += acc;
        }
    }
}