tor-browser

ellipse.rs (6061B)

---

/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */

use api::units::*;
use euclid::Size2D;
use std::f32::consts::FRAC_PI_2;


/// Number of steps to integrate arc length over.
const STEP_COUNT: usize = 20;

/// Represents an ellipse centred at a local space origin.
#[derive(Debug, Clone)]
pub struct Ellipse<U> {
   pub radius: Size2D<f32, U>,
   pub total_arc_length: f32,
}

impl<U> Ellipse<U> {
   pub fn new(radius: Size2D<f32, U>) -> Ellipse<U> {
       // Approximate the total length of the first quadrant of this ellipse.
       let total_arc_length = get_simpson_length(FRAC_PI_2, radius.width, radius.height);

       Ellipse {
           radius,
           total_arc_length,
       }
   }

   /// Binary search to estimate the angle of an ellipse
   /// for a given arc length. This only searches over the
   /// first quadrant of an ellipse.
   pub fn find_angle_for_arc_length(&self, arc_length: f32) -> f32 {
       // Clamp arc length to [0, pi].
       let arc_length = arc_length.max(0.0).min(self.total_arc_length);

       let epsilon = 0.01;
       let mut low = 0.0;
       let mut high = FRAC_PI_2;
       let mut theta = 0.0;
       let mut new_low = 0.0;
       let mut new_high = FRAC_PI_2;

       while low <= high {
           theta = 0.5 * (low + high);
           let length = get_simpson_length(theta, self.radius.width, self.radius.height);

           if (length - arc_length).abs() < epsilon {
               break;
           } else if length < arc_length {
               new_low = theta;
           } else {
               new_high = theta;
           }

           // If we have stopped moving down the arc, the answer that we have is as good as
           // it is going to get. We break to avoid going into an infinite loop.
           if new_low == low && new_high == high {
               break;
           }

           high = new_high;
           low = new_low;
       }

       theta
   }

   /// Get a point and tangent on this ellipse from a given angle.
   /// This only works for the first quadrant of the ellipse.
   pub fn get_point_and_tangent(&self, theta: f32) -> (LayoutPoint, LayoutPoint) {
       let (sin_theta, cos_theta) = theta.sin_cos();
       let point = LayoutPoint::new(
           self.radius.width * cos_theta,
           self.radius.height * sin_theta,
       );
       let tangent = LayoutPoint::new(
           -self.radius.width * sin_theta,
           self.radius.height * cos_theta,
       );
       (point, tangent)
   }

   pub fn contains(&self, point: LayoutPoint) -> bool {
       self.signed_distance(point.to_vector()) <= 0.0
   }

   /// Find the signed distance from this ellipse given a point.
   /// Taken from http://www.iquilezles.org/www/articles/ellipsedist/ellipsedist.htm
   fn signed_distance(&self, point: LayoutVector2D) -> f32 {
       // This algorithm fails for circles, so we handle them here.
       if self.radius.width == self.radius.height {
           return point.length() - self.radius.width;
       }

       let mut p = LayoutVector2D::new(point.x.abs(), point.y.abs());
       let mut ab = self.radius.to_vector();
       if p.x > p.y {
           p = p.yx();
           ab = ab.yx();
       }

       let l = ab.y * ab.y - ab.x * ab.x;

       let m = ab.x * p.x / l;
       let n = ab.y * p.y / l;
       let m2 = m * m;
       let n2 = n * n;

       let c = (m2 + n2 - 1.0) / 3.0;
       let c3 = c * c * c;

       let q = c3 + m2 * n2 * 2.0;
       let d = c3 + m2 * n2;
       let g = m + m * n2;

       let co = if d < 0.0 {
           let p = (q / c3).acos() / 3.0;
           let s = p.cos();
           let t = p.sin() * (3.0_f32).sqrt();
           let rx = (-c * (s + t + 2.0) + m2).sqrt();
           let ry = (-c * (s - t + 2.0) + m2).sqrt();
           (ry + l.signum() * rx + g.abs() / (rx * ry) - m) / 2.0
       } else {
           let h = 2.0 * m * n * d.sqrt();
           let s = (q + h).signum() * (q + h).abs().powf(1.0 / 3.0);
           let u = (q - h).signum() * (q - h).abs().powf(1.0 / 3.0);
           let rx = -s - u - c * 4.0 + 2.0 * m2;
           let ry = (s - u) * (3.0_f32).sqrt();
           let rm = (rx * rx + ry * ry).sqrt();
           let p = ry / (rm - rx).sqrt();
           (p + 2.0 * g / rm - m) / 2.0
       };

       let si = (1.0 - co * co).sqrt();
       let r = LayoutVector2D::new(ab.x * co, ab.y * si);
       (r - p).length() * (p.y - r.y).signum()
   }
}

/// Use Simpsons rule to approximate the arc length of
/// part of an ellipse. Note that this only works over
/// the range of [0, pi/2].
// TODO(gw): This is a simplistic way to estimate the
// arc length of an ellipse segment. We can probably use
// a faster / more accurate method!
fn get_simpson_length(theta: f32, rx: f32, ry: f32) -> f32 {
   let df = theta / STEP_COUNT as f32;
   let mut sum = 0.0;

   for i in 0 .. (STEP_COUNT + 1) {
       let (sin_theta, cos_theta) = (i as f32 * df).sin_cos();
       let a = rx * sin_theta;
       let b = ry * cos_theta;
       let y = (a * a + b * b).sqrt();
       let q = if i == 0 || i == STEP_COUNT {
           1.0
       } else if i % 2 == 0 {
           2.0
       } else {
           4.0
       };

       sum += q * y;
   }

   (df / 3.0) * sum
}

#[cfg(test)]
pub mod test {
   use super::*;

   #[test]
   fn find_angle_for_arc_length_for_long_eclipse() {
       // Ensure that finding the angle on giant ellipses produces and answer and
       // doesn't send us into an infinite loop.
       let ellipse = Ellipse::new(LayoutSize::new(57500.0, 25.0));
       let _ = ellipse.find_angle_for_arc_length(55674.53);
       assert!(true);

       let ellipse = Ellipse::new(LayoutSize::new(25.0, 57500.0));
       let _ = ellipse.find_angle_for_arc_length(55674.53);
       assert!(true);
   }
}