2 files changed, 126 insertions, 0 deletions
diff --git a/src/main/java/com/pau101/util/BezierUtils.java b/src/main/java/com/pau101/util/BezierUtils.java
new file mode 100644
index 0000000..eb52917
--- /dev/null
+++ b/src/main/java/com/pau101/util/BezierUtils.java
@@ -0,0 +1,98 @@
+package com.pau101.util;
+
+/**
+ * @author Paul Fulham (pau101)
+ */
+public final class BezierUtils
+{
+    private BezierUtils()
+    {}
+    
+    /**
+     * Compute the value of all nth degree Bernstein polynomials.
+     *
+     * @param curveDegree : degree of curve
+     * @param t : curve parameter on interval [0,1]
+     * @param scalars : curveDegree + 1 Bernstein values.
+     */
+    public static void allBernstein(int curveDegree, float t, float scalars[])
+    {
+        int j, k;
+        float nt = 1 - t;
+        float saved;
+        scalars[0] = 1;
+        for(j = 1; j <= curveDegree; j++){
+            saved = 0;
+            for(k = 0; k < j; k++){
+                float temp = scalars[k];
+                scalars[k] = saved + nt * temp;
+                saved = t * temp;
+            }
+            scalars[j] = saved;
+        }
+    }
+    
+    /**
+     * Compute point of nth degree Bezier curve.
+     *
+     * @param controlPoints : curveDegree + 1 control points
+     * @param curveDegree : degree of curve
+     * @param t : curve parameter on interval [0,1]
+     * @param point : resulting point
+     */
+    public static void pointOnBezierCurve(float controlPoints[][], int curveDegree, float t, float point[])
+    {
+        float scalars[] = new float[curveDegree + 1];
+        int k;
+        allBernstein(curveDegree, t, scalars);
+        point[0] = point[1] = point[2] = 0;
+        for(k = 0; k <= curveDegree; k++){
+            point[0] += scalars[k] * controlPoints[k][0];
+            point[1] += scalars[k] * controlPoints[k][1];
+            point[2] += scalars[k] * controlPoints[k][2];
+        }
+    }
+    
+    /**
+     * Compute an approximate length of a Bezier curve given the control points.
+     *
+     * @param controlPoints : control points of a Bezier curve
+     * @return the approximate length
+     */
+    public static float approximateLength(float controlPoints[][])
+    {
+        float length = 0;
+        for(int i = 0; i < controlPoints.length - 1; i++){
+            float xDif = controlPoints[i + 1][0] - controlPoints[i][0];
+            float yDif = controlPoints[i + 1][1] - controlPoints[i][1];
+            float zDif = controlPoints[i + 1][2] - controlPoints[i][2];
+            length += Math.sqrt(xDif * xDif + yDif * yDif + zDif * zDif);
+        }
+        return length;
+    }
+    
+    public static int tesselationSegementsForLength(float length, float scale)
+    {
+        float noLessThan = 10 * scale;
+        float segs = length * scale / 30F;
+        return (int)Math.ceil(Math.sqrt(segs * segs * 0.6 + noLessThan * noLessThan));
+    }
+    
+    public static float[][] curve(float controlPoints[][])
+    {
+        return curve(controlPoints, 1);
+    }
+    
+    public static float[][] curve(float controlPoints[][], float scale)
+    {
+        int count = tesselationSegementsForLength(approximateLength(controlPoints), scale);
+        float[][] points = new float[count][3];
+        for(int i = 0; i < count; i++){
+            float t = i / (float)(count - 1);
+            float[] point = new float[3];
+            pointOnBezierCurve(controlPoints, controlPoints.length - 1, t, point);
+            points[i] = point;
+        }
+        return points;
+    }
+}
+\ No newline at end of file
diff --git a/src/main/java/com/pau101/util/CubicBezier.java b/src/main/java/com/pau101/util/CubicBezier.java
new file mode 100644
index 0000000..aab2a98
--- /dev/null
+++ b/src/main/java/com/pau101/util/CubicBezier.java
@@ -0,0 +1,28 @@
+package com.pau101.util;
+
+/**
+ * @author Paul Fulham (pau101)
+ */
+public class CubicBezier
+{
+    private float[][] controlPoints;
+    
+    public CubicBezier(float a1, float b1, float a2, float b2)
+    {
+        controlPoints = new float[4][];
+        controlPoints[0] = new float[]{0, 0};
+        controlPoints[1] = new float[]{a1, b1};
+        controlPoints[2] = new float[]{a2, b2};
+        controlPoints[3] = new float[]{1, 1};
+    }
+    
+    public float eval(float t)
+    {
+        float[] scalars = new float[4];
+        BezierUtils.allBernstein(3, t, scalars);
+        float p = 0;
+        for(int i = 0; i < 4; i++)
+            p += scalars[i] * controlPoints[i][1];
+        return p;
+    }
+}
+\ No newline at end of file