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Bezier-rs: Updated Bezier function signatures to accept TValue (#967)
* Create helper for converting d to t values * Add euclidean option for tangent and normal * Modified bezier functions signatures to accept ComputeType * Stylistic changes per review * Added ComputeType documentation * Renamed ComputeType to TValue * Fixed comments * Fixed failing unit tests * Code review * Fix comments in code review * Renamed compute_type_to_parametric to t_value_to_parametric --------- Co-authored-by: Linda Zheng <thelindazheng@gmail.com> Co-authored-by: Keavon Chambers <keavon@keavon.com>
This commit is contained in:
Rob Nadal
co-authored by
Linda Zheng
Keavon Chambers
Linda Zheng
Keavon Chambers
parent
1c2b8f67b2
commit
76be1f8515
@@ -1,15 +1,16 @@
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use super::*;
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use crate::utils::ComputeType;
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use crate::utils::TValue;
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use glam::DMat2;
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use std::ops::Range;
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/// Functionality that solve for various curve information such as derivative, tangent, intersect, etc.
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impl Bezier {
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/// Returns a list of lists of points representing the De Casteljau points for all iterations at the point corresponding to `t` using De Casteljau's algorithm.
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/// Returns a list of lists of points representing the De Casteljau points for all iterations at the point `t` along the curve using De Casteljau's algorithm.
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/// The `i`th element of the list represents the set of points in the `i`th iteration.
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/// More information on the algorithm can be found in the [De Casteljau section](https://pomax.github.io/bezierinfo/#decasteljau) in Pomax's primer.
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pub fn de_casteljau_points(&self, t: f64) -> Vec<Vec<DVec2>> {
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pub fn de_casteljau_points(&self, t: TValue) -> Vec<Vec<DVec2>> {
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let t = self.t_value_to_parametric(t);
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let bezier_points = match self.handles {
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BezierHandles::Linear => vec![self.start, self.end],
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BezierHandles::Quadratic { handle } => vec![self.start, handle, self.end],
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@@ -30,7 +31,7 @@ impl Bezier {
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de_casteljau_points
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}
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/// Returns a Bezier representing the derivative of the original curve.
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/// Returns a [Bezier] representing the derivative of the original curve.
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/// - This function returns `None` for a linear segment.
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pub fn derivative(&self) -> Option<Bezier> {
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match self.handles {
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@@ -49,27 +50,29 @@ impl Bezier {
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}
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}
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/// Returns a normalized unit vector representing the tangent at the point designated by `t` on the curve.
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pub fn tangent(&self, t: f64) -> DVec2 {
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/// Returns a normalized unit vector representing the tangent at the point `t` along the curve.
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pub fn tangent(&self, t: TValue) -> DVec2 {
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let t = self.t_value_to_parametric(t);
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match self.handles {
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BezierHandles::Linear => self.end - self.start,
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_ => self.derivative().unwrap().evaluate(ComputeType::Parametric(t)),
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_ => self.derivative().unwrap().evaluate(TValue::Parametric(t)),
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}
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.normalize()
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}
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/// Returns a normalized unit vector representing the direction of the normal at the point designated by `t` on the curve.
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pub fn normal(&self, t: f64) -> DVec2 {
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/// Returns a normalized unit vector representing the direction of the normal at the point `t` along the curve.
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pub fn normal(&self, t: TValue) -> DVec2 {
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self.tangent(t).perp()
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}
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/// Returns the curvature, a scalar value for the derivative at the given `t`-value along the curve.
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/// Returns the curvature, a scalar value for the derivative at the point `t` along the curve.
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/// Curvature is 1 over the radius of a circle with an equivalent derivative.
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pub fn curvature(&self, t: f64) -> f64 {
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pub fn curvature(&self, t: TValue) -> f64 {
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let t = self.t_value_to_parametric(t);
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let (d, dd) = match &self.derivative() {
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Some(first_derivative) => match first_derivative.derivative() {
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Some(second_derivative) => (first_derivative.evaluate(ComputeType::Parametric(t)), second_derivative.evaluate(ComputeType::Parametric(t))),
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None => (first_derivative.evaluate(ComputeType::Parametric(t)), first_derivative.end - first_derivative.start),
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Some(second_derivative) => (first_derivative.evaluate(TValue::Parametric(t)), second_derivative.evaluate(TValue::Parametric(t))),
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None => (first_derivative.evaluate(TValue::Parametric(t)), first_derivative.end - first_derivative.start),
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},
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None => (self.end - self.start, DVec2::new(0., 0.)),
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};
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@@ -129,7 +132,7 @@ impl Bezier {
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let extrema = self.local_extrema();
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for t_values in extrema {
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for t in t_values {
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let point = self.evaluate(ComputeType::Parametric(t));
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let point = self.evaluate(TValue::Parametric(t));
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// Update bounding box if new min/max is found.
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endpoints_min = endpoints_min.min(point);
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endpoints_max = endpoints_max.max(point);
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@@ -178,7 +181,7 @@ impl Bezier {
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}
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}
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/// Returns list of `t`-values representing the inflection points of the curve.
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/// Returns list of parametric `t`-values representing the inflection points of the curve.
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/// The list of `t`-values returned are filtered such that they fall within the range `[0, 1]`.
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pub fn inflections(&self) -> Vec<f64> {
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self.unrestricted_inflections().into_iter().filter(|&t| t > 0. && t < 1.).collect::<Vec<f64>>()
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@@ -213,8 +216,8 @@ impl Bezier {
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}
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// Split curves in half and repeat with the combinations of the two halves of each curve
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let [split_1_a, split_1_b] = self.split(0.5);
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let [split_2_a, split_2_b] = other.split(0.5);
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let [split_1_a, split_1_b] = self.split(TValue::Parametric(0.5));
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let [split_2_a, split_2_b] = other.split(TValue::Parametric(0.5));
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[
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split_1_a.intersections_between_subcurves(self_start_t..self_mid_t, &split_2_a, other_start_t..other_mid_t, error),
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@@ -229,7 +232,7 @@ impl Bezier {
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}
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// TODO: Use an `impl Iterator` return type instead of a `Vec`
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/// Returns a list of filtered `t` values that correspond to intersection points between the current bezier curve and the provided one
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/// Returns a list of filtered parametric `t` values that correspond to intersection points between the current bezier curve and the provided one
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/// such that the difference between adjacent `t` values in sorted order is greater than some minimum seperation value. If the difference
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/// between 2 adjacent `t` values is lesss than the minimum difference, the filtering takes the larger `t` value and discards the smaller `t` value.
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/// The returned `t` values are with respect to the current bezier, not the provided parameter.
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@@ -242,8 +245,6 @@ impl Bezier {
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let mut intersection_t_values = self.unfiltered_intersections(other, error);
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intersection_t_values.sort_by(|a, b| a.partial_cmp(b).unwrap());
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// println!("<<<<< intersection_t_values :: {:?}", intersection_t_values);
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intersection_t_values.iter().fold(Vec::new(), |mut accumulator, t| {
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if !accumulator.is_empty() && (accumulator.last().unwrap() - t).abs() < minimum_seperation.unwrap_or(MIN_SEPERATION_VALUE) {
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accumulator.pop();
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@@ -334,7 +335,7 @@ impl Bezier {
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}
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// TODO: Use an `impl Iterator` return type instead of a `Vec`
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/// Returns a list of `t` values that correspond to the self intersection points of the current bezier curve. For each intersection point, the returned `t` value is the smaller of the two that correspond to the point.
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/// Returns a list of parametric `t` values that correspond to the self intersection points of the current bezier curve. For each intersection point, the returned `t` value is the smaller of the two that correspond to the point.
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/// - `error` - For intersections with non-linear beziers, `error` defines the threshold for bounding boxes to be considered an intersection point.
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pub fn self_intersections(&self, error: Option<f64>) -> Vec<[f64; 2]> {
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if self.handles == BezierHandles::Linear || matches!(self.handles, BezierHandles::Quadratic { .. }) {
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@@ -362,7 +363,7 @@ impl Bezier {
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.collect()
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}
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/// Returns a list of `t` values that correspond to the intersection points between the curve and a rectangle defined by opposite corners.
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/// Returns a list of parametric `t` values that correspond to the intersection points between the curve and a rectangle defined by opposite corners.
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pub fn rectangle_intersections(&self, corner1: DVec2, corner2: DVec2) -> Vec<f64> {
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[
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Bezier::from_linear_coordinates(corner1.x, corner1.y, corner2.x, corner1.y),
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@@ -384,7 +385,7 @@ mod tests {
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#[test]
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fn test_de_casteljau_points() {
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let bezier = Bezier::from_cubic_coordinates(0., 0., 0., 100., 100., 100., 100., 0.);
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let de_casteljau_points = bezier.de_casteljau_points(0.5);
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let de_casteljau_points = bezier.de_casteljau_points(TValue::Parametric(0.5));
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let expected_de_casteljau_points = vec![
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vec![DVec2::new(0., 0.), DVec2::new(0., 100.), DVec2::new(100., 100.), DVec2::new(100., 0.)],
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vec![DVec2::new(0., 50.), DVec2::new(50., 100.), DVec2::new(100., 50.)],
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@@ -393,7 +394,7 @@ mod tests {
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];
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assert_eq!(&de_casteljau_points, &expected_de_casteljau_points);
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assert_eq!(expected_de_casteljau_points[3][0], bezier.evaluate(ComputeType::Parametric(0.5)));
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assert_eq!(expected_de_casteljau_points[3][0], bezier.evaluate(TValue::Parametric(0.5)));
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}
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#[test]
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@@ -433,16 +434,16 @@ mod tests {
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let linear = Bezier::from_linear_dvec2(p1, p2);
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let unit_slope = DVec2::new(30., 20.).normalize();
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assert_eq!(linear.tangent(0.), unit_slope);
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assert_eq!(linear.tangent(1.), unit_slope);
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assert_eq!(linear.tangent(TValue::Parametric(0.)), unit_slope);
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assert_eq!(linear.tangent(TValue::Parametric(1.)), unit_slope);
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let quadratic = Bezier::from_quadratic_dvec2(p1, p2, p3);
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assert_eq!(quadratic.tangent(0.), DVec2::new(60., 40.).normalize());
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assert_eq!(quadratic.tangent(1.), DVec2::new(40., 60.).normalize());
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assert_eq!(quadratic.tangent(TValue::Parametric(0.)), DVec2::new(60., 40.).normalize());
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assert_eq!(quadratic.tangent(TValue::Parametric(1.)), DVec2::new(40., 60.).normalize());
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let cubic = Bezier::from_cubic_dvec2(p1, p2, p3, p4);
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assert_eq!(cubic.tangent(0.), DVec2::new(90., 60.).normalize());
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assert_eq!(cubic.tangent(1.), DVec2::new(30., 120.).normalize());
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assert_eq!(cubic.tangent(TValue::Parametric(0.)), DVec2::new(90., 60.).normalize());
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assert_eq!(cubic.tangent(TValue::Parametric(1.)), DVec2::new(30., 120.).normalize());
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}
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#[test]
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@@ -455,16 +456,16 @@ mod tests {
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let linear = Bezier::from_linear_dvec2(p1, p2);
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let unit_slope = DVec2::new(-20., 30.).normalize();
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assert_eq!(linear.normal(0.), unit_slope);
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assert_eq!(linear.normal(1.), unit_slope);
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assert_eq!(linear.normal(TValue::Parametric(0.)), unit_slope);
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assert_eq!(linear.normal(TValue::Parametric(1.)), unit_slope);
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let quadratic = Bezier::from_quadratic_dvec2(p1, p2, p3);
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assert_eq!(quadratic.normal(0.), DVec2::new(-40., 60.).normalize());
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assert_eq!(quadratic.normal(1.), DVec2::new(-60., 40.).normalize());
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assert_eq!(quadratic.normal(TValue::Parametric(0.)), DVec2::new(-40., 60.).normalize());
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assert_eq!(quadratic.normal(TValue::Parametric(1.)), DVec2::new(-60., 40.).normalize());
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let cubic = Bezier::from_cubic_dvec2(p1, p2, p3, p4);
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assert_eq!(cubic.normal(0.), DVec2::new(-60., 90.).normalize());
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assert_eq!(cubic.normal(1.), DVec2::new(-120., 30.).normalize());
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assert_eq!(cubic.normal(TValue::Parametric(0.)), DVec2::new(-60., 90.).normalize());
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assert_eq!(cubic.normal(TValue::Parametric(1.)), DVec2::new(-120., 30.).normalize());
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}
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#[test]
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@@ -475,24 +476,24 @@ mod tests {
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let p4 = DVec2::new(50., 10.);
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let linear = Bezier::from_linear_dvec2(p1, p2);
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assert_eq!(linear.curvature(0.), 0.);
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assert_eq!(linear.curvature(0.5), 0.);
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assert_eq!(linear.curvature(1.), 0.);
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assert_eq!(linear.curvature(TValue::Parametric(0.)), 0.);
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assert_eq!(linear.curvature(TValue::Parametric(0.5)), 0.);
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assert_eq!(linear.curvature(TValue::Parametric(1.)), 0.);
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let quadratic = Bezier::from_quadratic_dvec2(p1, p2, p3);
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assert!(compare_f64s(quadratic.curvature(0.), 0.0125));
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assert!(compare_f64s(quadratic.curvature(0.5), 0.035355));
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assert!(compare_f64s(quadratic.curvature(1.), 0.0125));
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assert!(compare_f64s(quadratic.curvature(TValue::Parametric(0.)), 0.0125));
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assert!(compare_f64s(quadratic.curvature(TValue::Parametric(0.5)), 0.035355));
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assert!(compare_f64s(quadratic.curvature(TValue::Parametric(1.)), 0.0125));
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let cubic = Bezier::from_cubic_dvec2(p1, p2, p3, p4);
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assert!(compare_f64s(cubic.curvature(0.), 0.016667));
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assert!(compare_f64s(cubic.curvature(0.5), 0.));
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assert!(compare_f64s(cubic.curvature(1.), 0.));
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assert!(compare_f64s(cubic.curvature(TValue::Parametric(0.)), 0.016667));
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assert!(compare_f64s(cubic.curvature(TValue::Parametric(0.5)), 0.));
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assert!(compare_f64s(cubic.curvature(TValue::Parametric(1.)), 0.));
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// The curvature at an inflection point is zero
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let inflection_curve = Bezier::from_cubic_coordinates(30., 30., 30., 150., 150., 30., 150., 150.);
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let inflections = inflection_curve.inflections();
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assert_eq!(inflection_curve.curvature(inflections[0]), 0.);
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assert_eq!(inflection_curve.curvature(TValue::Parametric(inflections[0])), 0.);
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}
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#[test]
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@@ -609,12 +610,12 @@ mod tests {
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let line1 = Bezier::from_linear_coordinates(20., 60., 70., 60.);
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let intersections1 = bezier.intersections(&line1, None, None);
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assert!(intersections1.len() == 1);
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assert!(compare_points(bezier.evaluate(ComputeType::Parametric(intersections1[0])), DVec2::new(30., 60.)));
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assert!(compare_points(bezier.evaluate(TValue::Parametric(intersections1[0])), DVec2::new(30., 60.)));
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// Intersection in the middle of curve
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let line2 = Bezier::from_linear_coordinates(150., 150., 30., 30.);
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let intersections2 = bezier.intersections(&line2, None, None);
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assert!(compare_points(bezier.evaluate(ComputeType::Parametric(intersections2[0])), DVec2::new(96., 96.)));
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assert!(compare_points(bezier.evaluate(TValue::Parametric(intersections2[0])), DVec2::new(96., 96.)));
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}
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#[test]
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@@ -628,12 +629,12 @@ mod tests {
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let line1 = Bezier::from_linear_coordinates(20., 50., 40., 50.);
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let intersections1 = bezier.intersections(&line1, None, None);
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assert!(intersections1.len() == 1);
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assert!(compare_points(bezier.evaluate(ComputeType::Parametric(intersections1[0])), p1));
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assert!(compare_points(bezier.evaluate(TValue::Parametric(intersections1[0])), p1));
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// Intersection in the middle of curve
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let line2 = Bezier::from_linear_coordinates(150., 150., 30., 30.);
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let intersections2 = bezier.intersections(&line2, None, None);
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assert!(compare_points(bezier.evaluate(ComputeType::Parametric(intersections2[0])), DVec2::new(47.77355, 47.77354)));
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assert!(compare_points(bezier.evaluate(TValue::Parametric(intersections2[0])), DVec2::new(47.77355, 47.77354)));
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}
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#[test]
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@@ -648,14 +649,14 @@ mod tests {
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let line1 = Bezier::from_linear_coordinates(20., 30., 40., 30.);
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let intersections1 = bezier.intersections(&line1, None, None);
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assert!(intersections1.len() == 1);
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assert!(compare_points(bezier.evaluate(ComputeType::Parametric(intersections1[0])), p1));
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assert!(compare_points(bezier.evaluate(TValue::Parametric(intersections1[0])), p1));
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// Intersection at edge and in middle of curve, Discriminant < 0
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let line2 = Bezier::from_linear_coordinates(150., 150., 30., 30.);
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let intersections2 = bezier.intersections(&line2, None, None);
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assert!(intersections2.len() == 2);
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assert!(compare_points(bezier.evaluate(ComputeType::Parametric(intersections2[0])), p1));
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assert!(compare_points(bezier.evaluate(ComputeType::Parametric(intersections2[1])), DVec2::new(85.84, 85.84)));
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assert!(compare_points(bezier.evaluate(TValue::Parametric(intersections2[0])), p1));
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assert!(compare_points(bezier.evaluate(TValue::Parametric(intersections2[1])), DVec2::new(85.84, 85.84)));
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}
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#[test]
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@@ -672,7 +673,7 @@ mod tests {
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let intersections = bezier.intersections(&line, None, None);
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assert_eq!(intersections.len(), 1);
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assert!(compare_points(bezier.evaluate(ComputeType::Parametric(intersections[0])), p4));
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assert!(compare_points(bezier.evaluate(TValue::Parametric(intersections[0])), p4));
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}
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#[test]
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@@ -699,8 +700,8 @@ mod tests {
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let intersections1 = bezier1.intersections(&bezier2, None, None);
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let intersections2 = bezier2.intersections(&bezier1, None, None);
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let intersections1_points: Vec<DVec2> = intersections1.iter().map(|&t| bezier1.evaluate(ComputeType::Parametric(t))).collect();
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let intersections2_points: Vec<DVec2> = intersections2.iter().map(|&t| bezier2.evaluate(ComputeType::Parametric(t))).rev().collect();
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let intersections1_points: Vec<DVec2> = intersections1.iter().map(|&t| bezier1.evaluate(TValue::Parametric(t))).collect();
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let intersections2_points: Vec<DVec2> = intersections2.iter().map(|&t| bezier2.evaluate(TValue::Parametric(t))).rev().collect();
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assert!(compare_vec_of_points(intersections1_points, intersections2_points, 2.));
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}
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@@ -710,8 +711,8 @@ mod tests {
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let bezier = Bezier::from_cubic_coordinates(160., 180., 170., 10., 30., 90., 180., 140.);
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let intersections = bezier.self_intersections(Some(0.5));
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assert!(compare_vec_of_points(
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intersections.iter().map(|&t| bezier.evaluate(ComputeType::Parametric(t[0]))).collect(),
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intersections.iter().map(|&t| bezier.evaluate(ComputeType::Parametric(t[1]))).collect(),
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intersections.iter().map(|&t| bezier.evaluate(TValue::Parametric(t[0]))).collect(),
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intersections.iter().map(|&t| bezier.evaluate(TValue::Parametric(t[1]))).collect(),
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2.
|
||||
));
|
||||
assert!(Bezier::from_linear_coordinates(160., 180., 170., 10.).self_intersections(None).is_empty());
|
||||
|
||||
Reference in New Issue
Block a user