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//! Glyph outlines
//!
//! Coordinates stay in font units, and y points up. When written out, the coordinates are
//! multiplied by the size, and y is flipped.
use crate::text::number;
/// One segment that makes up an outline
#[derive(Debug, Clone, PartialEq)]
pub enum Segment {
/// Moves to a point without drawing
Move {x: f64, y: f64},
/// A straight line
Line {x: f64, y: f64},
/// A quadratic Bezier curve. TrueType glyphs use it
Quadratic {x1: f64, y1: f64, x: f64, y: f64},
/// A cubic Bezier curve. CFF glyphs use it
Cubic {x1: f64, y1: f64, x2: f64, y2: f64, x: f64, y: f64},
/// Closes the outline currently being drawn
Close,
}
/// The outline of one glyph
#[derive(Debug, Clone, Default, PartialEq)]
pub struct Outline {
pub segment: Vec<Segment>,
}
/// The box around an outline, as (left, bottom, right, top). All 0 if there is no segment
pub fn bounds(outline: &Outline) -> (f64, f64, f64, f64) {
let mut left = f64::INFINITY;
let mut bottom = f64::INFINITY;
let mut right = f64::NEG_INFINITY;
let mut top = f64::NEG_INFINITY;
let mut current = (0.0, 0.0);
let mut start = (0.0, 0.0);
let mut touched = false;
let mut take = |x: f64, y: f64| {
left = left.min(x);
bottom = bottom.min(y);
right = right.max(x);
top = top.max(y);
};
for segment in &outline.segment {
match segment {
Segment::Move {x, y} => {
current = (*x, *y);
start = current;
}
Segment::Line {x, y} => {
take(current.0, current.1);
take(*x, *y);
current = (*x, *y);
touched = true;
}
Segment::Quadratic {x1, y1, x, y} => {
take(current.0, current.1);
take(*x, *y);
take_quadratic((current.0, *x1, *x), (current.1, *y1, *y), &mut take);
current = (*x, *y);
touched = true;
}
Segment::Cubic {x1, y1, x2, y2, x, y} => {
take(current.0, current.1);
take(*x, *y);
take_cubic(
(current.0, *x1, *x2, *x),
(current.1, *y1, *y2, *y),
&mut take,
);
current = (*x, *y);
touched = true;
}
Segment::Close => current = start,
}
}
if !touched {
return (0.0, 0.0, 0.0, 0.0);
}
(left, bottom, right, top)
}
/// Takes the extrema of a quadratic Bezier curve that are not at its ends
fn take_quadratic(x: (f64, f64, f64), y: (f64, f64, f64), take: &mut impl FnMut(f64, f64)) {
let mut at = |t: f64| {
take(quadratic_at(x.0, x.1, x.2, t), quadratic_at(y.0, y.1, y.2, t));
};
if let Some(t) = quadratic_turn(x.0, x.1, x.2) {
at(t);
}
if let Some(t) = quadratic_turn(y.0, y.1, y.2) {
at(t);
}
}
/// Takes the extrema of a cubic Bezier curve that are not at its ends
fn take_cubic(x: (f64, f64, f64, f64), y: (f64, f64, f64, f64), take: &mut impl FnMut(f64, f64)) {
for t in cubic_turn(x.0, x.1, x.2, x.3) {
take(cubic_at(x.0, x.1, x.2, x.3, t), cubic_at(y.0, y.1, y.2, y.3, t));
}
for t in cubic_turn(y.0, y.1, y.2, y.3) {
take(cubic_at(x.0, x.1, x.2, x.3, t), cubic_at(y.0, y.1, y.2, y.3, t));
}
}
fn quadratic_at(p0: f64, p1: f64, p2: f64, t: f64) -> f64 {
let s = 1.0 - t;
s * s * p0 + 2.0 * s * t * p1 + t * t * p2
}
fn cubic_at(p0: f64, p1: f64, p2: f64, p3: f64, t: f64) -> f64 {
let s = 1.0 - t;
s * s * s * p0 + 3.0 * s * s * t * p1 + 3.0 * s * t * t * p2 + t * t * t * p3
}
/// The t at which the derivative of a quadratic Bezier curve is 0. Returns it only if it is
/// between 0 and 1
fn quadratic_turn(p0: f64, p1: f64, p2: f64) -> Option<f64> {
let bottom = p0 - 2.0 * p1 + p2;
if bottom.abs() < 1e-12 {
return None;
}
let t = (p0 - p1) / bottom;
if t > 0.0 && t < 1.0 {Some(t)} else {None}
}
/// The values of t at which the derivative of a cubic Bezier curve is 0. Returns only those
/// between 0 and 1
fn cubic_turn(p0: f64, p1: f64, p2: f64, p3: f64) -> Vec<f64> {
let a = 3.0 * (-p0 + 3.0 * p1 - 3.0 * p2 + p3);
let b = 6.0 * (p0 - 2.0 * p1 + p2);
let c = 3.0 * (p1 - p0);
let mut found = Vec::new();
if a.abs() < 1e-12 {
if b.abs() > 1e-12 {
found.push(-c / b);
}
} else {
let discriminant = b * b - 4.0 * a * c;
if discriminant >= 0.0 {
let root = discriminant.sqrt();
found.push((-b + root) / (2.0 * a));
found.push((-b - root) / (2.0 * a));
}
}
found.retain(|t| *t > 0.0 && *t < 1.0);
found
}
/// Writes an outline as an SVG d attribute. Multiplies by scale, flips y, and places it at
/// (offsetX, offsetY)
pub fn path_data(outline: &Outline, scale: f64, offset_x: f64, offset_y: f64) -> String {
let mut out = String::new();
let place = |x: f64, y: f64| {
format!("{} {}", number(offset_x + x * scale), number(offset_y - y * scale))
};
for segment in &outline.segment {
match segment {
Segment::Move {x, y} => {
out.push('M');
out.push_str(&place(*x, *y));
}
Segment::Line {x, y} => {
out.push('L');
out.push_str(&place(*x, *y));
}
Segment::Quadratic {x1, y1, x, y} => {
out.push('Q');
out.push_str(&place(*x1, *y1));
out.push(' ');
out.push_str(&place(*x, *y));
}
Segment::Cubic {x1, y1, x2, y2, x, y} => {
out.push('C');
out.push_str(&place(*x1, *y1));
out.push(' ');
out.push_str(&place(*x2, *y2));
out.push(' ');
out.push_str(&place(*x, *y));
}
Segment::Close => out.push('Z'),
}
}
out
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn a_straight_box() {
let outline = Outline {
segment: vec![
Segment::Move {x: 10.0, y: 20.0},
Segment::Line {x: 100.0, y: 20.0},
Segment::Line {x: 100.0, y: 200.0},
Segment::Close,
],
};
assert_eq!(bounds(&outline), (10.0, 20.0, 100.0, 200.0));
}
#[test]
fn a_curve_reaches_past_its_control_points() {
// Returns the box of the curve itself, not the box of its control points
let outline = Outline {
segment: vec![
Segment::Move {x: 0.0, y: 0.0},
Segment::Quadratic {x1: 50.0, y1: 100.0, x: 100.0, y: 0.0},
],
};
let (left, bottom, right, top) = bounds(&outline);
assert_eq!((left, bottom, right), (0.0, 0.0, 100.0));
assert!((top - 50.0).abs() < 1e-9);
}
#[test]
fn a_cubic_curve_too() {
let outline = Outline {
segment: vec![
Segment::Move {x: 0.0, y: 0.0},
Segment::Cubic {x1: 0.0, y1: 100.0, x2: 100.0, y2: 100.0, x: 100.0, y: 0.0},
],
};
let (_, bottom, _, top) = bounds(&outline);
assert_eq!(bottom, 0.0);
assert!((top - 75.0).abs() < 1e-9);
}
#[test]
fn an_empty_outline_has_no_box() {
assert_eq!(bounds(&Outline::default()), (0.0, 0.0, 0.0, 0.0));
}
#[test]
fn writes_a_path_with_the_y_flipped() {
let outline = Outline {
segment: vec![
Segment::Move {x: 0.0, y: 500.0},
Segment::Line {x: 1000.0, y: 0.0},
Segment::Close,
],
};
assert_eq!(path_data(&outline, 0.001, 0.0, 0.0), "M0 -0.5L1 0Z");
}
}