leibniz 0.2.0

The package provides a differentiable vector graphics rasterization loss.
Documentation 
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//! Boundary geometry.

use ::burn::tensor::{Bool, Int, Tensor, TensorData, backend::Backend};

use crate::{
    base::geometry::Command,
    burn::geometry::{Basis, Contour, Coordinates, contour, left_normals, quadratic_basis},
};

use super::distribution::{Records, SegmentIndices, UnitSamples};

const EPSILON: f32 = 1e-6;

/// Boundary PDF with shape `[samples]`.
pub type Pdf<B> = Tensor<B, 1>;

/// Boundary point index columns with shapes `[samples]`, indexing the
/// control points flattened to `[segments * 2]`.
pub type Indices<B> = (Tensor<B, 1, Int>, Tensor<B, 1, Int>, Tensor<B, 1, Int>);

/// Control point coordinate columns with shapes `[samples]`.
type Points<B> = (Coordinates<B>, Coordinates<B>, Coordinates<B>);

/// Boundary geometry for sampled quadratic points.
pub struct Geometry<B: Backend> {
    // Downstream signal and jump code consumes coordinate columns directly, so
    // keep points and normals column-wise instead of rebuilding point matrices.
    points: Coordinates<B>,
    normals: Coordinates<B>,
    pdf: Pdf<B>,
    basis: Basis<B>,
    indices: Indices<B>,
}

impl<B: Backend> Geometry<B> {
    /// Argument weights.
    pub fn basis(&self) -> Basis<B> {
        self.basis.clone()
    }

    /// Boundary point index columns.
    pub fn indices(&self) -> Indices<B> {
        self.indices.clone()
    }

    /// Boundary normal coordinate columns.
    pub fn normals(&self) -> Coordinates<B> {
        self.normals.clone()
    }

    /// Boundary PDF.
    pub fn pdf(&self) -> Pdf<B> {
        self.pdf.clone()
    }

    /// Boundary point coordinate columns.
    pub fn points(&self) -> Coordinates<B> {
        self.points.clone()
    }
}

/// Evaluate boundary geometry for sampled records.
///
/// # Panics
///
/// Panics if the contour is empty, does not have segment shape
/// `[segments, 2, 2]`, or does not match the sampled records.
pub fn evaluate<B: Backend>(contour: Contour<B>, records: &Records<B>) -> Geometry<B> {
    let [segment_count, point_count, coordinate_count] = contour.dims();

    assert!(
        segment_count > 0
            && point_count == 2
            && coordinate_count == 2
            && contour.commands().len() == segment_count
            && segment_count == records.segment_count(),
        "commands and arguments must match sampled records for a non-empty contour"
    );

    let t = records.t();
    let segment_indices = records.segment_indices();
    let linear_mask = linear_mask(contour.commands(), segment_indices.clone(), &t.device());
    let end_segment_indices =
        (segment_indices.clone() + 1).remainder_scalar(segment_count as i64);
    let indices = indices(segment_indices.clone(), end_segment_indices.clone());
    let control_points = control_points(contour.arguments(), segment_indices, end_segment_indices);
    // Build basis columns directly; creating the basis matrix and slicing it back
    // into columns showed up as avoidable slice/copy work in profiles.
    let basis = basis(t.clone(), linear_mask.clone());
    let points = evaluate_points(control_points.clone(), basis.clone());
    let (normals, tangent_lengths) = evaluate_normals(control_points, t, linear_mask);
    let pdf = records.segment_pmf() / tangent_lengths.clone().clamp_min(EPSILON);

    Geometry {
        points,
        normals,
        pdf,
        basis,
        indices,
    }
}

fn basis<B: Backend>(t: UnitSamples<B>, linear_mask: Tensor<B, 1, Bool>) -> Basis<B> {
    let (quadratic0, quadratic1, quadratic2) = quadratic_basis(t.clone());
    let linear0 = t.ones_like() - t.clone();
    let linear1 = t.zeros_like();
    let linear2 = t;

    (
        quadratic0.mask_where(linear_mask.clone(), linear0),
        quadratic1.mask_where(linear_mask.clone(), linear1),
        quadratic2.mask_where(linear_mask, linear2),
    )
}

fn control_points<B: Backend>(
    arguments: contour::Arguments<B>,
    segment_indices: SegmentIndices<B>,
    end_segment_indices: SegmentIndices<B>,
) -> Points<B> {
    let segment_count = arguments.dims()[0];
    // Gather coordinate columns straight from the flattened arguments; the
    // former `[samples, 2]` point gathers were sliced back into columns, which
    // profiles showed as avoidable slice and copy work. The `[segments, 2, 2]`
    // arguments flatten to four values per segment in the order start x,
    // start y, control x, control y, and a segment's end point is the next
    // segment's start. Gather instead of select: the backend select funnels
    // the index tensor through a per-element iterator into a vector before
    // the lookup, measuring several times slower than gather for
    // sample-sized lookups.
    let flat = arguments.reshape([segment_count * 4]);
    let start = segment_indices * 4;
    let end = end_segment_indices * 4;
    let p0 = (
        flat.clone().gather(0, start.clone()),
        flat.clone().gather(0, start.clone() + 1),
    );
    let p1 = (
        flat.clone().gather(0, start.clone() + 2),
        flat.clone().gather(0, start + 3),
    );
    let p2 = (flat.clone().gather(0, end.clone()), flat.gather(0, end + 1));

    (p0, p1, p2)
}

fn evaluate_normals<B: Backend>(
    control_points: Points<B>,
    t: UnitSamples<B>,
    linear_mask: Tensor<B, 1, Bool>,
) -> (Coordinates<B>, Tensor<B, 1>) {
    let ((p0_x, p0_y), (p1_x, p1_y), (p2_x, p2_y)) = control_points;
    let u = t.ones_like() - t.clone();
    let t0 = u * 2.0;
    let t1 = t * 2.0;
    let tangent_x = ((p1_x.clone() - p0_x.clone()) * t0.clone()
        + (p2_x.clone() - p1_x) * t1.clone())
    .mask_where(linear_mask.clone(), p2_x - p0_x);
    let tangent_y = ((p1_y.clone() - p0_y.clone()) * t0 + (p2_y.clone() - p1_y) * t1)
        .mask_where(linear_mask, p2_y - p0_y);
    let tangent_lengths =
        (tangent_x.clone().powi_scalar(2) + tangent_y.clone().powi_scalar(2)).sqrt();
    let normals = left_normals((tangent_x, tangent_y), tangent_lengths.clone(), EPSILON);

    (normals, tangent_lengths)
}

fn evaluate_points<B: Backend>(control_points: Points<B>, basis: Basis<B>) -> Coordinates<B> {
    let ((p0_x, p0_y), (p1_x, p1_y), (p2_x, p2_y)) = control_points;
    let (b0, b1, b2) = basis;

    (
        p0_x * b0.clone() + p1_x * b1.clone() + p2_x * b2.clone(),
        p0_y * b0 + p1_y * b1 + p2_y * b2,
    )
}

fn indices<B: Backend>(
    segment_indices: SegmentIndices<B>,
    end_segment_indices: SegmentIndices<B>,
) -> Indices<B> {
    // A segment's start is point zero and its control point one of the
    // flattened `[segments * 2]` points; its end is the next segment's start.
    let start = segment_indices * 2;
    let control = start.clone() + 1;
    let end = end_segment_indices * 2;

    (start, control, end)
}

fn linear_mask<B: Backend>(
    commands: &[Command],
    segment_indices: Tensor<B, 1, Int>,
    device: &B::Device,
) -> Tensor<B, 1, Bool> {
    let values = commands
        .iter()
        .map(|command| matches!(command, Command::Linear))
        .collect::<Vec<_>>();

    Tensor::<B, 1, Bool>::from_data(TensorData::new(values, [commands.len()]), device)
        .gather(0, segment_indices)
}

#[cfg(test)]
mod tests {
    use super::super::{
        distribution::distribution,
        tests::{assert_floats, assert_ints, one_segment, samples, triangle},
    };
    use super::evaluate;
    use crate::burn::tests::Backend;

    #[test]
    fn evaluates_quadratic_boundary_geometry() {
        let segments = triangle();
        let distribution = distribution::<Backend>(segments.clone());
        let records = distribution.sample(samples([0.125, 5.0 / 12.0, 19.0 / 24.0]));
        let geometry = evaluate(segments, &records);

        let (point_x, point_y) = geometry.points();
        let (normal_x, normal_y) = geometry.normals();
        assert_floats(point_x, [1.5, 3.0, 1.5]);
        assert_floats(point_y, [0.0, 2.0, 2.0]);
        assert_floats(normal_x, [0.0, -1.0, 0.8]);
        assert_floats(normal_y, [1.0, 0.0, -0.6]);
        assert_floats(geometry.pdf(), [1.0 / 12.0, 1.0 / 12.0, 1.0 / 12.0]);
        let (b0, b1, b2) = geometry.basis();
        assert_floats(b0, [0.25, 0.25, 0.25]);
        assert_floats(b1, [0.5, 0.5, 0.5]);
        assert_floats(b2, [0.25, 0.25, 0.25]);
        let (start, control, end) = geometry.indices();
        assert_ints(start, [0, 2, 4]);
        assert_ints(control, [1, 3, 5]);
        assert_ints(end, [2, 4, 0]);
    }

    #[test]
    #[should_panic]
    fn rejects_mismatched_boundary_records() {
        let distribution = distribution::<Backend>(triangle());
        let records = distribution.sample(samples([0.125]));

        let _ = evaluate(one_segment(), &records);
    }
}