Implement math `cancel` function (#793)

2 files changed, 172 insertions, 0 deletions

diff --git a/library/src/math/cancel.rs b/library/src/math/cancel.rs
new file mode 100644
index 00000000..0ea7b1d2
--- /dev/null
+++ b/library/src/math/cancel.rs
@@ -0,0 +1,169 @@
+use super::*;
+
+/// Displays a diagonal line over a part of an equation.
+///
+/// ## Example
+/// ```example
+/// Here, we can simplify:
+/// $ (a dot.c b dot.c cancel(x)) / cancel(x) $
+/// ```
+///
+/// Display: Cancel
+/// Category: math
+#[element(LayoutMath)]
+pub struct CancelElem {
+    /// The content over which the line should be placed.
+    #[required]
+    pub body: Content,
+
+    /// The length of the line, relative to the length of the diagonal spanning
+    /// the whole element being "cancelled". A value of `{100%}` would then have
+    /// the line span precisely the element's diagonal.
+    ///
+    /// Defaults to `{100% + 3pt}`.
+    ///
+    /// ```example
+    /// $ a + cancel(x, length: #200%) - b - cancel(x, length: #200%) $
+    /// ```
+    #[default(Rel::new(Ratio::one(), Abs::pt(3.0).into()))]
+    pub length: Rel<Length>,
+
+    /// If the cancel line should be inverted (heading northwest instead of
+    /// northeast).
+    ///
+    /// Defaults to `{false}`.
+    ///
+    /// ```example
+    /// $ (a cancel((b + c), inverted: #true)) / cancel(b + c, inverted: #true) $
+    /// ```
+    #[default(false)]
+    pub inverted: bool,
+
+    /// If two opposing cancel lines should be drawn, forming a cross over the
+    /// element. Overrides `inverted`.
+    ///
+    /// Defaults to `{false}`.
+    ///
+    /// ```example
+    /// $ cancel(x, cross: #true) $
+    /// ```
+    #[default(false)]
+    pub cross: bool,
+
+    /// Rotate the cancel line by a certain angle. See the
+    /// [line's documentation]($func/line.angle) for more details.
+    ///
+    /// ```example
+    /// $ cancel(x, rotation: #30deg) $
+    /// ```
+    #[default(Angle::zero())]
+    pub rotation: Angle,
+
+    /// How to stroke the cancel line. See the
+    /// [line's documentation]($func/line.stroke) for more details.
+    ///
+    /// ```example
+    /// $ cancel(x, stroke: #{red + 1.5pt}) $
+    /// ```
+    #[resolve]
+    #[fold]
+    pub stroke: PartialStroke,
+}
+
+impl LayoutMath for CancelElem {
+    fn layout_math(&self, ctx: &mut MathContext) -> SourceResult<()> {
+        let mut body = ctx.layout_frame(&self.body())?;
+
+        let styles = ctx.styles();
+        let body_size = body.size();
+        let span = self.span();
+        let length = self.length(styles).resolve(styles);
+
+        // Default stroke has 0.5pt for better visuals.
+        let stroke = self.stroke(styles).unwrap_or(Stroke {
+            paint: TextElem::fill_in(styles),
+            thickness: Abs::pt(0.5),
+            ..Default::default()
+        });
+
+        let invert = self.inverted(styles);
+        let cross = self.cross(styles);
+        let angle = self.rotation(styles);
+
+        let invert_first_line = !cross && invert;
+        let first_line = draw_cancel_line(
+            length,
+            stroke.clone(),
+            invert_first_line,
+            angle,
+            body_size,
+            span,
+        );
+
+        // The origin of our line is the very middle of the element.
+        let center = body_size.to_point() / 2.0;
+        body.push_frame(center, first_line);
+
+        if cross {
+            // Draw the second line.
+            let second_line =
+                draw_cancel_line(length, stroke, true, angle, body_size, span);
+
+            body.push_frame(center, second_line);
+        }
+
+        ctx.push(FrameFragment::new(ctx, body));
+
+        Ok(())
+    }
+}
+
+/// Draws a cancel line.
+fn draw_cancel_line(
+    length: Rel<Abs>,
+    stroke: Stroke,
+    invert: bool,
+    angle: Angle,
+    body_size: Size,
+    span: Span,
+) -> Frame {
+    //            B
+    //           /|
+    // diagonal / | height
+    //         /  |
+    //        /   |
+    //       O ----
+    //         width
+    let diagonal = body_size.to_point().hypot();
+    let length = length.relative_to(diagonal);
+    let (width, height) = (body_size.x, body_size.y);
+    let mid = body_size / 2.0;
+
+    // Scale the amount needed such that the cancel line has the given 'length'
+    // (reference length, or 100%, is the whole diagonal).
+    // Scales from the center.
+    let scale = length.to_raw() / diagonal.to_raw();
+
+    // invert horizontally if 'invert' was given
+    let scale_x = scale * if invert { -1.0 } else { 1.0 };
+    let scale_y = scale;
+    let scales = Axes::new(scale_x, scale_y);
+
+    // Draw a line from bottom left to top right of the given element, where the
+    // origin represents the very middle of that element, that is, a line from
+    // (-width / 2, height / 2) with length components (width, -height) (sign is
+    // inverted in the y-axis). After applying the scale, the line will have the
+    // correct length and orientation (inverted if needed).
+    let start = Axes::new(-mid.x, mid.y).zip(scales).map(|(l, s)| l * s);
+    let delta = Axes::new(width, -height).zip(scales).map(|(l, s)| l * s);
+
+    let mut frame = Frame::new(body_size);
+    frame.push(
+        start.to_point(),
+        FrameItem::Shape(Geometry::Line(delta.to_point()).stroked(stroke), span),
+    );
+
+    // Having the middle of the line at the origin is convenient here.
+    frame.transform(Transform::rotate(angle));
+    frame
+}
diff --git a/library/src/math/mod.rs b/library/src/math/mod.rs
index 9c8a9cdf..48fe52d2 100644
--- a/library/src/math/mod.rs
+++ b/library/src/math/mod.rs
@@ -5,6 +5,7 @@ mod ctx;
 mod accent;
 mod align;
 mod attach;
+mod cancel;
 mod delimited;
 mod frac;
 mod fragment;
@@ -20,6 +21,7 @@ mod underover;
 pub use self::accent::*;
 pub use self::align::*;
 pub use self::attach::*;
+pub use self::cancel::*;
 pub use self::delimited::*;
 pub use self::frac::*;
 pub use self::matrix::*;
@@ -71,6 +73,7 @@ pub fn module() -> Module {
     math.define("overbrace", OverbraceElem::func());
     math.define("underbracket", UnderbracketElem::func());
     math.define("overbracket", OverbracketElem::func());
+    math.define("cancel", CancelElem::func());
 
     // Fractions and matrix-likes.
     math.define("frac", FracElem::func());