use super::*; use crate::consts::MIN_SEPERATION_VALUE; use crate::utils::SubpathTValue; use crate::TValue; use glam::DVec2; impl Subpath { /// Calculate the point on the subpath based on the parametric `t`-value provided. /// Expects `t` to be within the inclusive range `[0, 1]`. /// pub fn evaluate(&self, t: SubpathTValue) -> DVec2 { let (segment_index, t) = self.t_value_to_parametric(t); self.get_segment(segment_index).unwrap().evaluate(TValue::Parametric(t)) } /// Calculates the intersection points the subpath has with a given curve and returns a list of parameteric `t`-values. /// This function expects the following: /// - other: a [Bezier] curve to check intersections against /// - error: an optional f64 value to provide an error bound /// pub fn intersections(&self, other: &Bezier, error: Option, minimum_seperation: Option) -> Vec { // TODO: account for either euclidean or parametric type let number_of_curves = self.len_segments() as f64; let intersection_t_values: Vec = self .iter() .enumerate() .flat_map(|(index, bezier)| { bezier .intersections(other, error, minimum_seperation) .into_iter() .map(|t| ((index as f64) + t) / number_of_curves) .collect::>() }) .collect(); intersection_t_values.iter().fold(Vec::new(), |mut accumulator, t| { if !accumulator.is_empty() && (accumulator.last().unwrap() - t).abs() < minimum_seperation.unwrap_or(MIN_SEPERATION_VALUE) { accumulator.pop(); } accumulator.push(*t); accumulator }); intersection_t_values } /// Returns a normalized unit vector representing the tangent on the subpath based on the parametric `t`-value provided. /// pub fn tangent(&self, t: SubpathTValue) -> DVec2 { let (segment_index, t) = self.t_value_to_parametric(t); self.get_segment(segment_index).unwrap().tangent(TValue::Parametric(t)) } /// Returns a normalized unit vector representing the direction of the normal on the subpath based on the parametric `t`-value provided. /// pub fn normal(&self, t: SubpathTValue) -> DVec2 { let (segment_index, t) = self.t_value_to_parametric(t); self.get_segment(segment_index).unwrap().normal(TValue::Parametric(t)) } } #[cfg(test)] mod tests { use super::*; use crate::Bezier; use glam::DVec2; use crate::consts::MAX_ABSOLUTE_DIFFERENCE; use crate::utils; fn normalize_t(n: i64, t: f64) -> f64 { t * (n as f64) % 1. } #[test] fn evaluate_one_subpath_curve() { let start = DVec2::new(20., 30.); let end = DVec2::new(60., 45.); let handle = DVec2::new(75., 85.); let bezier = Bezier::from_quadratic_dvec2(start, handle, end); let subpath = Subpath::new( vec![ ManipulatorGroup { anchor: start, in_handle: None, out_handle: Some(handle), }, ManipulatorGroup { anchor: end, in_handle: None, out_handle: Some(handle), }, ], false, ); let t0 = 0.; assert_eq!(subpath.evaluate(SubpathTValue::GlobalParametric(t0)), bezier.evaluate(TValue::Parametric(t0))); let t1 = 0.25; assert_eq!(subpath.evaluate(SubpathTValue::GlobalParametric(t1)), bezier.evaluate(TValue::Parametric(t1))); let t2 = 0.50; assert_eq!(subpath.evaluate(SubpathTValue::GlobalParametric(t2)), bezier.evaluate(TValue::Parametric(t2))); let t3 = 1.; assert_eq!(subpath.evaluate(SubpathTValue::GlobalParametric(t3)), bezier.evaluate(TValue::Parametric(t3))); } #[test] fn evaluate_multiple_subpath_curves() { let start = DVec2::new(20., 30.); let middle = DVec2::new(70., 70.); let end = DVec2::new(60., 45.); let handle1 = DVec2::new(75., 85.); let handle2 = DVec2::new(40., 30.); let handle3 = DVec2::new(10., 10.); let linear_bezier = Bezier::from_linear_dvec2(start, middle); let quadratic_bezier = Bezier::from_quadratic_dvec2(middle, handle1, end); let cubic_bezier = Bezier::from_cubic_dvec2(end, handle2, handle3, start); let mut subpath = Subpath::new( vec![ ManipulatorGroup { anchor: start, in_handle: Some(handle3), out_handle: None, }, ManipulatorGroup { anchor: middle, in_handle: None, out_handle: Some(handle1), }, ManipulatorGroup { anchor: end, in_handle: None, out_handle: Some(handle2), }, ], false, ); // Test open subpath let mut n = (subpath.len() as i64) - 1; let t0 = 0.; assert!(utils::dvec2_compare( subpath.evaluate(SubpathTValue::GlobalParametric(t0)), linear_bezier.evaluate(TValue::Parametric(normalize_t(n, t0))), MAX_ABSOLUTE_DIFFERENCE ) .all()); let t1 = 0.25; assert!(utils::dvec2_compare( subpath.evaluate(SubpathTValue::GlobalParametric(t1)), linear_bezier.evaluate(TValue::Parametric(normalize_t(n, t1))), MAX_ABSOLUTE_DIFFERENCE ) .all()); let t2 = 0.50; assert!(utils::dvec2_compare( subpath.evaluate(SubpathTValue::GlobalParametric(t2)), quadratic_bezier.evaluate(TValue::Parametric(normalize_t(n, t2))), MAX_ABSOLUTE_DIFFERENCE ) .all()); let t3 = 0.75; assert!(utils::dvec2_compare( subpath.evaluate(SubpathTValue::GlobalParametric(t3)), quadratic_bezier.evaluate(TValue::Parametric(normalize_t(n, t3))), MAX_ABSOLUTE_DIFFERENCE ) .all()); let t4 = 1.0; assert!(utils::dvec2_compare( subpath.evaluate(SubpathTValue::GlobalParametric(t4)), quadratic_bezier.evaluate(TValue::Parametric(1.)), MAX_ABSOLUTE_DIFFERENCE ) .all()); // Test closed subpath subpath.closed = true; n = subpath.len() as i64; let t5 = 2. / 3.; assert!(utils::dvec2_compare( subpath.evaluate(SubpathTValue::GlobalParametric(t5)), cubic_bezier.evaluate(TValue::Parametric(normalize_t(n, t5))), MAX_ABSOLUTE_DIFFERENCE ) .all()); let t6 = 1.; assert!(utils::dvec2_compare( subpath.evaluate(SubpathTValue::GlobalParametric(t6)), cubic_bezier.evaluate(TValue::Parametric(1.)), MAX_ABSOLUTE_DIFFERENCE ) .all()); } #[test] fn intersection_linear_multiple_subpath_curves_test_one() { // M 35 125 C 40 40 120 120 43 43 Q 175 90 145 150 Q 70 185 35 125 Z let cubic_start = DVec2::new(35., 125.); let cubic_handle_1 = DVec2::new(40., 40.); let cubic_handle_2 = DVec2::new(120., 120.); let cubic_end = DVec2::new(43., 43.); let quadratic_1_handle = DVec2::new(175., 90.); let quadratic_end = DVec2::new(145., 150.); let quadratic_2_handle = DVec2::new(70., 185.); let cubic_bezier = Bezier::from_cubic_dvec2(cubic_start, cubic_handle_1, cubic_handle_2, cubic_end); let quadratic_bezier_1 = Bezier::from_quadratic_dvec2(cubic_end, quadratic_1_handle, quadratic_end); let subpath = Subpath::new( vec![ ManipulatorGroup { anchor: cubic_start, in_handle: None, out_handle: Some(cubic_handle_1), }, ManipulatorGroup { anchor: cubic_end, in_handle: Some(cubic_handle_2), out_handle: None, }, ManipulatorGroup { anchor: quadratic_end, in_handle: Some(quadratic_1_handle), out_handle: Some(quadratic_2_handle), }, ], true, ); let line = Bezier::from_linear_coordinates(150., 150., 20., 20.); let cubic_intersections = cubic_bezier.intersections(&line, None, None); let quadratic_1_intersections = quadratic_bezier_1.intersections(&line, None, None); let subpath_intersections = subpath.intersections(&line, None, None); assert!(utils::dvec2_compare( cubic_bezier.evaluate(TValue::Parametric(cubic_intersections[0])), subpath.evaluate(SubpathTValue::GlobalParametric(subpath_intersections[0])), MAX_ABSOLUTE_DIFFERENCE ) .all()); assert!(utils::dvec2_compare( quadratic_bezier_1.evaluate(TValue::Parametric(quadratic_1_intersections[0])), subpath.evaluate(SubpathTValue::GlobalParametric(subpath_intersections[1])), MAX_ABSOLUTE_DIFFERENCE ) .all()); assert!(utils::dvec2_compare( quadratic_bezier_1.evaluate(TValue::Parametric(quadratic_1_intersections[1])), subpath.evaluate(SubpathTValue::GlobalParametric(subpath_intersections[2])), MAX_ABSOLUTE_DIFFERENCE ) .all()); } #[test] fn intersection_linear_multiple_subpath_curves_test_two() { // M34 107 C40 40 120 120 102 29 Q175 90 129 171 Q70 185 34 107 Z // M150 150 L 20 20 let cubic_start = DVec2::new(34., 107.); let cubic_handle_1 = DVec2::new(40., 40.); let cubic_handle_2 = DVec2::new(120., 120.); let cubic_end = DVec2::new(102., 29.); let quadratic_1_handle = DVec2::new(175., 90.); let quadratic_end = DVec2::new(129., 171.); let quadratic_2_handle = DVec2::new(70., 185.); let cubic_bezier = Bezier::from_cubic_dvec2(cubic_start, cubic_handle_1, cubic_handle_2, cubic_end); let quadratic_bezier_1 = Bezier::from_quadratic_dvec2(cubic_end, quadratic_1_handle, quadratic_end); let subpath = Subpath::new( vec![ ManipulatorGroup { anchor: cubic_start, in_handle: None, out_handle: Some(cubic_handle_1), }, ManipulatorGroup { anchor: cubic_end, in_handle: Some(cubic_handle_2), out_handle: None, }, ManipulatorGroup { anchor: quadratic_end, in_handle: Some(quadratic_1_handle), out_handle: Some(quadratic_2_handle), }, ], true, ); let line = Bezier::from_linear_coordinates(150., 150., 20., 20.); let cubic_intersections = cubic_bezier.intersections(&line, None, None); let quadratic_1_intersections = quadratic_bezier_1.intersections(&line, None, None); let subpath_intersections = subpath.intersections(&line, None, None); assert!(utils::dvec2_compare( cubic_bezier.evaluate(TValue::Parametric(cubic_intersections[0])), subpath.evaluate(SubpathTValue::GlobalParametric(subpath_intersections[0])), MAX_ABSOLUTE_DIFFERENCE ) .all()); assert!(utils::dvec2_compare( quadratic_bezier_1.evaluate(TValue::Parametric(quadratic_1_intersections[0])), subpath.evaluate(SubpathTValue::GlobalParametric(subpath_intersections[1])), MAX_ABSOLUTE_DIFFERENCE ) .all()); } #[test] fn intersection_linear_multiple_subpath_curves_test_three() { // M35 125 C40 40 120 120 44 44 Q175 90 145 150 Q70 185 35 125 Z let cubic_start = DVec2::new(35., 125.); let cubic_handle_1 = DVec2::new(40., 40.); let cubic_handle_2 = DVec2::new(120., 120.); let cubic_end = DVec2::new(44., 44.); let quadratic_1_handle = DVec2::new(175., 90.); let quadratic_end = DVec2::new(145., 150.); let quadratic_2_handle = DVec2::new(70., 185.); let cubic_bezier = Bezier::from_cubic_dvec2(cubic_start, cubic_handle_1, cubic_handle_2, cubic_end); let quadratic_bezier_1 = Bezier::from_quadratic_dvec2(cubic_end, quadratic_1_handle, quadratic_end); let subpath = Subpath::new( vec![ ManipulatorGroup { anchor: cubic_start, in_handle: None, out_handle: Some(cubic_handle_1), }, ManipulatorGroup { anchor: cubic_end, in_handle: Some(cubic_handle_2), out_handle: None, }, ManipulatorGroup { anchor: quadratic_end, in_handle: Some(quadratic_1_handle), out_handle: Some(quadratic_2_handle), }, ], true, ); let line = Bezier::from_linear_coordinates(150., 150., 20., 20.); let cubic_intersections = cubic_bezier.intersections(&line, None, None); let quadratic_1_intersections = quadratic_bezier_1.intersections(&line, None, None); let subpath_intersections = subpath.intersections(&line, None, None); assert!(utils::dvec2_compare( cubic_bezier.evaluate(TValue::Parametric(cubic_intersections[0])), subpath.evaluate(SubpathTValue::GlobalParametric(subpath_intersections[0])), MAX_ABSOLUTE_DIFFERENCE ) .all()); assert!(utils::dvec2_compare( quadratic_bezier_1.evaluate(TValue::Parametric(quadratic_1_intersections[0])), subpath.evaluate(SubpathTValue::GlobalParametric(subpath_intersections[1])), MAX_ABSOLUTE_DIFFERENCE ) .all()); assert!(utils::dvec2_compare( quadratic_bezier_1.evaluate(TValue::Parametric(quadratic_1_intersections[1])), subpath.evaluate(SubpathTValue::GlobalParametric(subpath_intersections[2])), MAX_ABSOLUTE_DIFFERENCE ) .all()); } // TODO: add more intersection tests }