Improved geometry finding to be more pedagogical. Minor modifications to remove some warnings.

src/lib.rs

@@ -30,7 +30,7 @@ use cga::CGA;
 
 const PI: f64 = f64::consts::PI;
 const TWO_PI: f64 = 2.*PI;
-const ERROR: f64 = 0.0001;
+const ERROR: f64 = 0.000001;
 
 const WIDTH: f64 = 600.;
 const HEIGHT: f64 = 600.;
@@ -144,7 +144,7 @@ impl Ship {
         let com_p = com * gen_hyperbolic_point(&CGA::zero()) * com.Reverse();
         let delta_gen = com * orient_rotor * CGA::e14() * &orient_rotor.Reverse() * com.Reverse();
         let dot = delta_gen | &com_p;
-        let line = CGA::e4() ^ com_p ^ dot ^ CGA::e3();
+        let line = CGA::e4() ^ com_p ^ dot;// ^ CGA::e3();
         draw_line(context, &line);
 
 
@@ -153,8 +153,7 @@ impl Ship {
 
 enum Geometry {
     Circle(f64, f64, f64), //x,y,r
-    Line(f64, f64, f64), //x,r,theta
-    Null,
+    Line(f64, f64, f64), //x,y,theta
 }
 
 /* Translation of a Euclidean Point. Need to use hyperbolic*/
@@ -242,33 +241,31 @@ fn get_point(point: &CGA) -> (f64, f64) {
     (x/norm, y/norm)
 }
 
-fn get_geometry(circle: &CGA) -> Geometry {
-    //Naively assume we are given a valid line/circle
+fn get_geometry(trivector: &CGA) -> Geometry {
+    let trivector = grade_selection(trivector, 3);
+    let i4 = CGA::e1() ^ CGA::e2() ^ CGA::e4() ^ CGA::e5(); //Left out e3 intentionally
+    let i2 = CGA::e1() ^ CGA::e2();
     let n_bar = CGA::e4() - CGA::e5();
     let n_vec = CGA::e4() + CGA::e5();
-    let dual = (&circle).Dual();
-    let l = (&dual | &n_vec)[SCALAR];
-    let c = (&dual | &n_bar)[SCALAR];
-    let a = (&dual | CGA::e1())[SCALAR];
-    let b = (&dual | CGA::e2())[SCALAR];
 
-    if l.abs() < ERROR {
-        //LINE
-        let theta = (-a).atan2(b);
-        let norm_sqr = a*a + b*b;
-        if norm_sqr < ERROR*ERROR {
-            return Geometry::Null;
-        }
-        let x = a*c/norm_sqr/2.;
-        let y = b*c/norm_sqr/2.;
-        return Geometry::Line(x,y,theta);
+    let wedge = &trivector ^ &n_vec;
+    let mag = magnitude(&wedge);
+    let dual = &trivector * &i4;
+    if mag < ERROR {
+        //Line
+        let d = 0.5*(&dual | &n_bar)[SCALAR];
+        let m = -1.*(&dual - 0.5*d*&n_vec)*&i2;
+        let theta = (m[E2]).atan2(m[E1]);
+        return Geometry::Line(0., -d/m[E1], theta);
     } else {
         //Circle
-        let c_x = a/l;
-        let c_y = b/l;
-        let r_sqr = c_x*c_x + c_y*c_y + c/l;
-        let r = r_sqr.sqrt();
-        return Geometry::Circle(-c_x, -c_y, r);
+        let normalize = -(&dual | &n_vec)[SCALAR];
+        let dual = dual * (1.0/normalize);
+        let center = &trivector * &n_vec * &trivector;
+        let (x,y) = get_point(&center);
+        let sqr = (&dual * &dual)[SCALAR];
+        let r = sqr.sqrt();
+        return Geometry::Circle(x, y, r);
     }
 }
 
@@ -292,13 +289,12 @@ fn draw_line(context: &CanvasRenderingContext2d, line: &CGA) {
                 context.move_to(canvas_x1, canvas_y1);
                 context.line_to(canvas_x2, canvas_y2);
             },
-            Geometry::Null => {},
     }
     context.stroke();
 }
 
 fn draw_line_between(context: &CanvasRenderingContext2d, a: &CGA, b: &CGA) {
-    let line = CGA::e4() ^ a ^ b ^ CGA::e3();
+    let line = CGA::e4() ^ a ^ b;
     let geometry = get_geometry(&line);
     context.begin_path();
     context.set_stroke_style_str(GREEN);
@@ -352,20 +348,20 @@ fn _get_hyperbolic_translation(vec: &CGA) -> CGA {
     t
 }
 
-enum CircleIntersection {
-    Two_Points(CGA, CGA),
-    One_Point(CGA),
+enum _CircleIntersection {
+    TwoPoints(CGA, CGA),
+    OnePoint(CGA),
     None,
 }
 
 /*fn get_circle_intersection(circle_1: &CGA, circle_2: &CGA) -> CircleIntersection {
-    if !circle_intersection(circle_1, circle_2) {
+    if !circle_intersection(;//circle_1, circle_2) {
         return CircleIntersection::None;
     }
     let n = CGA::e4() + CGA::e5();
 }*/
 
-fn circle_intersection(circle_1: &CGA, circle_2: &CGA) -> bool {
+fn _circle_intersection(circle_1: &CGA, circle_2: &CGA) -> bool {
     let circle_1 = grade_selection(circle_1, 4);
     let circle_2 = grade_selection(circle_2, 4);
     let meet = circle_1 & circle_2;
@@ -378,7 +374,7 @@ fn circle_intersection(circle_1: &CGA, circle_2: &CGA) -> bool {
     }
 }
 
-fn line_intersection(line_1: &CGA, line_2: &CGA) -> bool {
+fn _line_intersection(line_1: &CGA, line_2: &CGA) -> bool {
     let line_1 = grade_selection(line_1, 4);
     let line_2 = grade_selection(line_2, 4);
     let meet = line_1 & line_2;
@@ -390,8 +386,8 @@ fn line_intersection(line_1: &CGA, line_2: &CGA) -> bool {
     }
 }
 
-fn get_line_intersection(line_1: &CGA, line_2: &CGA) -> Option<CGA> {
-    if !line_intersection(line_1, line_2) {
+fn _get_line_intersection(line_1: &CGA, line_2: &CGA) -> Option<CGA> {
+    if !_line_intersection(line_1, line_2) {
         return None;
     }
     let n = CGA::e4() + CGA::e5();
@@ -489,7 +485,7 @@ impl Asteroid {
         Asteroid { circle, vel }
     }
 
-    fn new_from_coords(x: f64, y: f64, r: f64, vel: CGA) -> Asteroid {
+    fn _new_from_coords(x: f64, y: f64, r: f64, vel: CGA) -> Asteroid {
         let circle = circle_from_coords(x, y, r);
         Asteroid { circle, vel }
     }
@@ -561,6 +557,7 @@ impl Game {
         self.context.set_stroke_style_str(BLACK);
         self.context.arc(CENTER_X, CENTER_Y, RADIUS, 0., TWO_PI).unwrap();
         self.context.stroke();
+
         draw_line(&self.context, &self.boundary);
         self.ship.draw(&self.context);
         for asteroid in &self.asteroids {