350 lines
12 KiB
C#
350 lines
12 KiB
C#
/**
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This class demonstrates the code discussed in these two articles:
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http://devmag.org.za/2011/04/05/bzier-curves-a-tutorial/
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http://devmag.org.za/2011/06/23/bzier-path-algorithms/
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Use this code as you wish, at your own risk. If it blows up
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your computer, makes a plane crash, or otherwise cause damage,
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injury, or death, it is not my fault.
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@author Herman Tulleken, dev.mag.org.za
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*/
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using System.Collections.Generic;
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namespace UnityEngine.UI.Extensions
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{
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/**
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Class for representing a Bezier path, and methods for getting suitable points to
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draw the curve with line segments.
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*/
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public class BezierPath
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{
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public int SegmentsPerCurve = 10;
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public float MINIMUM_SQR_DISTANCE = 0.01f;
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// This corresponds to about 172 degrees, 8 degrees from a straight line
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public float DIVISION_THRESHOLD = -0.99f;
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private List<Vector2> controlPoints;
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private int curveCount; //how many bezier curves in this path?
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/**
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Constructs a new empty Bezier curve. Use one of these methods
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to add points: SetControlPoints, Interpolate, SamplePoints.
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*/
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public BezierPath()
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{
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controlPoints = new List<Vector2>();
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}
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/**
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Sets the control points of this Bezier path.
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Points 0-3 forms the first Bezier curve, points
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3-6 forms the second curve, etc.
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*/
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public void SetControlPoints(List<Vector2> newControlPoints)
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{
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controlPoints.Clear();
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controlPoints.AddRange(newControlPoints);
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curveCount = (controlPoints.Count - 1) / 3;
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}
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public void SetControlPoints(Vector2[] newControlPoints)
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{
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controlPoints.Clear();
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controlPoints.AddRange(newControlPoints);
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curveCount = (controlPoints.Count - 1) / 3;
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}
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/**
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Returns the control points for this Bezier curve.
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*/
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public List<Vector2> GetControlPoints()
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{
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return controlPoints;
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}
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/**
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Calculates a Bezier interpolated path for the given points.
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*/
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public void Interpolate(List<Vector2> segmentPoints, float scale)
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{
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controlPoints.Clear();
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if (segmentPoints.Count < 2)
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{
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return;
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}
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for (int i = 0; i < segmentPoints.Count; i++)
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{
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if (i == 0) // is first
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{
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Vector2 p1 = segmentPoints[i];
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Vector2 p2 = segmentPoints[i + 1];
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Vector2 tangent = (p2 - p1);
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Vector2 q1 = p1 + scale * tangent;
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controlPoints.Add(p1);
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controlPoints.Add(q1);
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}
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else if (i == segmentPoints.Count - 1) //last
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{
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Vector2 p0 = segmentPoints[i - 1];
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Vector2 p1 = segmentPoints[i];
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Vector2 tangent = (p1 - p0);
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Vector2 q0 = p1 - scale * tangent;
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controlPoints.Add(q0);
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controlPoints.Add(p1);
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}
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else
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{
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Vector2 p0 = segmentPoints[i - 1];
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Vector2 p1 = segmentPoints[i];
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Vector2 p2 = segmentPoints[i + 1];
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Vector2 tangent = (p2 - p0).normalized;
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Vector2 q0 = p1 - scale * tangent * (p1 - p0).magnitude;
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Vector2 q1 = p1 + scale * tangent * (p2 - p1).magnitude;
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controlPoints.Add(q0);
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controlPoints.Add(p1);
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controlPoints.Add(q1);
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}
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}
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curveCount = (controlPoints.Count - 1) / 3;
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}
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/**
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Sample the given points as a Bezier path.
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*/
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public void SamplePoints(List<Vector2> sourcePoints, float minSqrDistance, float maxSqrDistance, float scale)
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{
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if (sourcePoints.Count < 2)
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{
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return;
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}
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Stack<Vector2> samplePoints = new Stack<Vector2>();
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samplePoints.Push(sourcePoints[0]);
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Vector2 potentialSamplePoint = sourcePoints[1];
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int i = 2;
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for (i = 2; i < sourcePoints.Count; i++)
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{
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if (
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((potentialSamplePoint - sourcePoints[i]).sqrMagnitude > minSqrDistance) &&
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((samplePoints.Peek() - sourcePoints[i]).sqrMagnitude > maxSqrDistance))
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{
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samplePoints.Push(potentialSamplePoint);
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}
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potentialSamplePoint = sourcePoints[i];
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}
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//now handle last bit of curve
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Vector2 p1 = samplePoints.Pop(); //last sample point
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Vector2 p0 = samplePoints.Peek(); //second last sample point
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Vector2 tangent = (p0 - potentialSamplePoint).normalized;
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float d2 = (potentialSamplePoint - p1).magnitude;
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float d1 = (p1 - p0).magnitude;
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p1 = p1 + tangent * ((d1 - d2) / 2);
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samplePoints.Push(p1);
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samplePoints.Push(potentialSamplePoint);
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Interpolate(new List<Vector2>(samplePoints), scale);
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}
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/**
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Calculates a point on the path.
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@param curveIndex The index of the curve that the point is on. For example,
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the second curve (index 1) is the curve with control points 3, 4, 5, and 6.
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@param t The parameter indicating where on the curve the point is. 0 corresponds
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to the "left" point, 1 corresponds to the "right" end point.
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*/
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public Vector2 CalculateBezierPoint(int curveIndex, float t)
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{
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int nodeIndex = curveIndex * 3;
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Vector2 p0 = controlPoints[nodeIndex];
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Vector2 p1 = controlPoints[nodeIndex + 1];
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Vector2 p2 = controlPoints[nodeIndex + 2];
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Vector2 p3 = controlPoints[nodeIndex + 3];
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return CalculateBezierPoint(t, p0, p1, p2, p3);
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}
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/**
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Gets the drawing points. This implementation simply calculates a certain number
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of points per curve.
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*/
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public List<Vector2> GetDrawingPoints0()
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{
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List<Vector2> drawingPoints = new List<Vector2>();
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for (int curveIndex = 0; curveIndex < curveCount; curveIndex++)
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{
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if (curveIndex == 0) //Only do this for the first end point.
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//When i != 0, this coincides with the
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//end point of the previous segment,
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{
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drawingPoints.Add(CalculateBezierPoint(curveIndex, 0));
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}
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for (int j = 1; j <= SegmentsPerCurve; j++)
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{
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float t = j / (float)SegmentsPerCurve;
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drawingPoints.Add(CalculateBezierPoint(curveIndex, t));
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}
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}
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return drawingPoints;
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}
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/**
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Gets the drawing points. This implementation simply calculates a certain number
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of points per curve.
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This is a slightly different implementation from the one above.
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*/
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public List<Vector2> GetDrawingPoints1()
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{
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List<Vector2> drawingPoints = new List<Vector2>();
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for (int i = 0; i < controlPoints.Count - 3; i += 3)
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{
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Vector2 p0 = controlPoints[i];
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Vector2 p1 = controlPoints[i + 1];
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Vector2 p2 = controlPoints[i + 2];
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Vector2 p3 = controlPoints[i + 3];
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if (i == 0) //only do this for the first end point. When i != 0, this coincides with the end point of the previous segment,
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{
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drawingPoints.Add(CalculateBezierPoint(0, p0, p1, p2, p3));
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}
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for (int j = 1; j <= SegmentsPerCurve; j++)
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{
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float t = j / (float)SegmentsPerCurve;
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drawingPoints.Add(CalculateBezierPoint(t, p0, p1, p2, p3));
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}
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}
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return drawingPoints;
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}
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/**
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This gets the drawing points of a bezier curve, using recursive division,
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which results in less points for the same accuracy as the above implementation.
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*/
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public List<Vector2> GetDrawingPoints2()
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{
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List<Vector2> drawingPoints = new List<Vector2>();
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for (int curveIndex = 0; curveIndex < curveCount; curveIndex++)
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{
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List<Vector2> bezierCurveDrawingPoints = FindDrawingPoints(curveIndex);
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if (curveIndex != 0)
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{
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//remove the fist point, as it coincides with the last point of the previous Bezier curve.
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bezierCurveDrawingPoints.RemoveAt(0);
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}
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drawingPoints.AddRange(bezierCurveDrawingPoints);
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}
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return drawingPoints;
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}
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List<Vector2> FindDrawingPoints(int curveIndex)
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{
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List<Vector2> pointList = new List<Vector2>();
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Vector2 left = CalculateBezierPoint(curveIndex, 0);
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Vector2 right = CalculateBezierPoint(curveIndex, 1);
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pointList.Add(left);
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pointList.Add(right);
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FindDrawingPoints(curveIndex, 0, 1, pointList, 1);
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return pointList;
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}
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/**
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@returns the number of points added.
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*/
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int FindDrawingPoints(int curveIndex, float t0, float t1,
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List<Vector2> pointList, int insertionIndex)
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{
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Vector2 left = CalculateBezierPoint(curveIndex, t0);
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Vector2 right = CalculateBezierPoint(curveIndex, t1);
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if ((left - right).sqrMagnitude < MINIMUM_SQR_DISTANCE)
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{
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return 0;
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}
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float tMid = (t0 + t1) / 2;
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Vector2 mid = CalculateBezierPoint(curveIndex, tMid);
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Vector2 leftDirection = (left - mid).normalized;
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Vector2 rightDirection = (right - mid).normalized;
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if (Vector2.Dot(leftDirection, rightDirection) > DIVISION_THRESHOLD || Mathf.Abs(tMid - 0.5f) < 0.0001f)
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{
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int pointsAddedCount = 0;
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pointsAddedCount += FindDrawingPoints(curveIndex, t0, tMid, pointList, insertionIndex);
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pointList.Insert(insertionIndex + pointsAddedCount, mid);
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pointsAddedCount++;
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pointsAddedCount += FindDrawingPoints(curveIndex, tMid, t1, pointList, insertionIndex + pointsAddedCount);
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return pointsAddedCount;
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}
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return 0;
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}
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/**
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Calculates a point on the Bezier curve represented with the four control points given.
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*/
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private Vector2 CalculateBezierPoint(float t, Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3)
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{
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float u = 1 - t;
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float tt = t * t;
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float uu = u * u;
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float uuu = uu * u;
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float ttt = tt * t;
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Vector2 p = uuu * p0; //first term
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p += 3 * uu * t * p1; //second term
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p += 3 * u * tt * p2; //third term
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p += ttt * p3; //fourth term
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return p;
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}
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}
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} |