Implement G1 and C1 curve conversion.

1 files changed, 32 insertions, 7 deletions

diff --git a/src/main.cpp b/src/main.cpp
index c658614..f5ee54a 100755
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -306,8 +306,8 @@ void
 make_curves_G1(const bezier_curve &s0, const bezier_curve &s1,
 	       bezier_curve &d0, bezier_curve &d1)
 {
-	/* FINISHME: Implement this function.
-	 */
+	GLUvec4 moved_point = s1[0] + (s0[3] - s0[2]);
+	d1 = bezier_curve(s1[0], moved_point, s1[2], s1[3]);
 }
 
 
@@ -327,8 +327,25 @@ void
 make_curves_C1(const bezier_curve &s0, const bezier_curve &s1,
 	       bezier_curve &d0, bezier_curve &d1)
 {
-	/* FINISHME: Implement this function.
+	/* The derivative of s0 at t = 1.0 is:
+	 *   3(s0[3] - s0[2])
+	 *
+	 * The derivative of s1 at t = 0.0 is:
+	 *   3(s1[1] - s1[0])
+	 *
+	 * To achieve C1 continuity, we need to make the curve differentiable
+	 * everywhere (in particular, at the joint point between these curves).
+	 * To do so, the two derivatives must be equal:
+	 *
+	 * 3(s1[1] - s1[0]) = 3(s0[3] - s0[2])
+	 *   s1[1] - s1[0]  =   s0[3] - s0[2]
+	 *
+	 * Notably since s0[3] = s1[0]
+	 *   s1[1] - s1[0]  =   s1[0] - s0[2]
+	 *   s1[1]          = 2*s1[0] - s0[2]
 	 */
+	GLUvec4 moved_point = s1[0] + 2*s1[0] - s0[2];
+	d1 = bezier_curve(s1[0], moved_point, s1[2], s1[3]);
 }
 
 
@@ -368,11 +385,19 @@ Init(void)
 	       "    c: Re-load and compile shader program code.\n"
 	       "  ESC: Exit program.\n");
 
-	/* FINISHME: Invoke make_curves_G1 here to fix the basic curves.
-	 */
+	for (int i = 0; i < 3; i++) {
+		camera_curves_G1[i] = camera_curves[i];
+		camera_curves_C1[i] = camera_curves[i];
+	}
 
-	/* FINISHME: Invoke make_curves_C1 here to fix the basic curves.
-	 */
+	for (int i = 0; i < 3; i++) {
+		int next = (i + 1) % 3;
+		make_curves_G1(camera_curves_G1[i], camera_curves_G1[next],
+			       camera_curves_G1[i], camera_curves_G1[next]);
+
+		make_curves_C1(camera_curves_C1[i], camera_curves_C1[next],
+			       camera_curves_C1[i], camera_curves_C1[next]);
+	}
 }