// MIT License - Copyright (C) The Mono.Xna Team
// This file is subject to the terms and conditions defined in
// file 'LICENSE.txt', which is part of this source code package.
using System;
using System.ComponentModel;
using System.Runtime.Serialization;
namespace CommonLang.Geometry
{
/// <summary>
/// Contains a collection of <see cref="CurveKey"/> points in 2D space and provides methods for evaluating features of the curve they define.
/// </summary>
// TODO : [TypeConverter(typeof(ExpandableObjectConverter))]
public class Curve
{
#region Private Fields
private CurveKeyCollection _keys;
private CurveLoopType _postLoop;
private CurveLoopType _preLoop;
#endregion
#region Public Properties
/// <summary>
/// Returns <c>true</c> if this curve is constant (has zero or one points); <c>false</c> otherwise.
/// </summary>
public bool IsConstant
{
get { return this._keys.Count <= 1; }
}
/// <summary>
/// The collection of curve keys.
/// </summary>
public CurveKeyCollection Keys
{
get { return this._keys; }
}
/// <summary>
/// Defines how to handle weighting values that are greater than the last control point in the curve.
/// </summary>
public CurveLoopType PostLoop
{
get { return this._postLoop; }
set { this._postLoop = value; }
}
/// <summary>
/// Defines how to handle weighting values that are less than the first control point in the curve.
/// </summary>
public CurveLoopType PreLoop
{
get { return this._preLoop; }
set { this._preLoop = value; }
}
#endregion
#region Public Constructors
/// <summary>
/// Constructs a curve.
/// </summary>
public Curve()
{
this._keys = new CurveKeyCollection();
}
#endregion
#region Public Methods
/// <summary>
/// Creates a copy of this curve.
/// </summary>
/// <returns>A copy of this curve.</returns>
public Curve Clone()
{
Curve curve = new Curve();
curve._keys = this._keys.Clone();
curve._preLoop = this._preLoop;
curve._postLoop = this._postLoop;
return curve;
}
/// <summary>
/// Evaluate the value at a position of this <see cref="Curve"/>.
/// </summary>
/// <param name="position">The position on this <see cref="Curve"/>.</param>
/// <returns>Value at the position on this <see cref="Curve"/>.</returns>
public float Evaluate(float position)
{
CurveKey first = _keys[0];
CurveKey last = _keys[_keys.Count - 1];
if (position < first.Position)
{
switch (this.PreLoop)
{
case CurveLoopType.Constant:
//constant
return first.Value;
case CurveLoopType.Linear:
// linear y = a*x +b with a tangeant of last point
return first.Value - first.TangentIn * (first.Position - position);
case CurveLoopType.Cycle:
//start -> end / start -> end
int cycle = GetNumberOfCycle(position);
float virtualPos = position - (cycle * (last.Position - first.Position));
return GetCurvePosition(virtualPos);
case CurveLoopType.CycleOffset:
//make the curve continue (with no step) so must up the curve each cycle of delta(value)
cycle = GetNumberOfCycle(position);
virtualPos = position - (cycle * (last.Position - first.Position));
return (GetCurvePosition(virtualPos) + cycle * (last.Value - first.Value));
case CurveLoopType.Oscillate:
//go back on curve from end and target start
// start-> end / end -> start
cycle = GetNumberOfCycle(position);
if (0 == cycle % 2f)//if pair
virtualPos = position - (cycle * (last.Position - first.Position));
else
virtualPos = last.Position - position + first.Position + (cycle * (last.Position - first.Position));
return GetCurvePosition(virtualPos);
}
}
else if (position > last.Position)
{
int cycle;
switch (this.PostLoop)
{
case CurveLoopType.Constant:
//constant
return last.Value;
case CurveLoopType.Linear:
// linear y = a*x +b with a tangeant of last point
return last.Value + first.TangentOut * (position - last.Position);
case CurveLoopType.Cycle:
//start -> end / start -> end
cycle = GetNumberOfCycle(position);
float virtualPos = position - (cycle * (last.Position - first.Position));
return GetCurvePosition(virtualPos);
case CurveLoopType.CycleOffset:
//make the curve continue (with no step) so must up the curve each cycle of delta(value)
cycle = GetNumberOfCycle(position);
virtualPos = position - (cycle * (last.Position - first.Position));
return (GetCurvePosition(virtualPos) + cycle * (last.Value - first.Value));
case CurveLoopType.Oscillate:
//go back on curve from end and target start
// start-> end / end -> start
cycle = GetNumberOfCycle(position);
virtualPos = position - (cycle * (last.Position - first.Position));
if (0 == cycle % 2f)//if pair
virtualPos = position - (cycle * (last.Position - first.Position));
else
virtualPos = last.Position - position + first.Position + (cycle * (last.Position - first.Position));
return GetCurvePosition(virtualPos);
}
}
//in curve
return GetCurvePosition(position);
}
/// <summary>
/// Computes tangents for all keys in the collection.
/// </summary>
/// <param name="tangentType">The tangent type for both in and out.</param>
public void ComputeTangents (CurveTangent tangentType)
{
ComputeTangents(tangentType, tangentType);
}
/// <summary>
/// Computes tangents for all keys in the collection.
/// </summary>
/// <param name="tangentInType">The tangent in-type. <see cref="CurveKey.TangentIn"/> for more details.</param>
/// <param name="tangentOutType">The tangent out-type. <see cref="CurveKey.TangentOut"/> for more details.</param>
public void ComputeTangents(CurveTangent tangentInType, CurveTangent tangentOutType)
{
for (var i = 0; i < Keys.Count; ++i)
{
ComputeTangent(i, tangentInType, tangentOutType);
}
}
/// <summary>
/// Computes tangent for the specific key in the collection.
/// </summary>
/// <param name="keyIndex">The index of a key in the collection.</param>
/// <param name="tangentType">The tangent type for both in and out.</param>
public void ComputeTangent(int keyIndex, CurveTangent tangentType)
{
ComputeTangent(keyIndex, tangentType, tangentType);
}
/// <summary>
/// Computes tangent for the specific key in the collection.
/// </summary>
/// <param name="keyIndex">The index of key in the collection.</param>
/// <param name="tangentInType">The tangent in-type. <see cref="CurveKey.TangentIn"/> for more details.</param>
/// <param name="tangentOutType">The tangent out-type. <see cref="CurveKey.TangentOut"/> for more details.</param>
public void ComputeTangent(int keyIndex, CurveTangent tangentInType, CurveTangent tangentOutType)
{
// See http://msdn.microsoft.com/en-us/library/microsoft.xna.framework.curvetangent.aspx
var key = _keys[keyIndex];
float p0, p, p1;
p0 = p = p1 = key.Position;
float v0, v, v1;
v0 = v = v1 = key.Value;
if ( keyIndex > 0 )
{
p0 = _keys[keyIndex - 1].Position;
v0 = _keys[keyIndex - 1].Value;
}
if (keyIndex < _keys.Count-1)
{
p1 = _keys[keyIndex + 1].Position;
v1 = _keys[keyIndex + 1].Value;
}
switch (tangentInType)
{
case CurveTangent.Flat:
key.TangentIn = 0;
break;
case CurveTangent.Linear:
key.TangentIn = v - v0;
break;
case CurveTangent.Smooth:
var pn = p1 - p0;
if (Math.Abs(pn) < float.Epsilon)
key.TangentIn = 0;
else
key.TangentIn = (v1 - v0) * ((p - p0) / pn);
break;
}
switch (tangentOutType)
{
case CurveTangent.Flat:
key.TangentOut = 0;
break;
case CurveTangent.Linear:
key.TangentOut = v1 - v;
break;
case CurveTangent.Smooth:
var pn = p1 - p0;
if (Math.Abs(pn) < float.Epsilon)
key.TangentOut = 0;
else
key.TangentOut = (v1 - v0) * ((p1 - p) / pn);
break;
}
}
#endregion
#region Private Methods
private int GetNumberOfCycle(float position)
{
float cycle = (position - _keys[0].Position) / (_keys[_keys.Count - 1].Position - _keys[0].Position);
if (cycle < 0f)
cycle--;
return (int)cycle;
}
private float GetCurvePosition(float position)
{
//only for position in curve
CurveKey prev = this._keys[0];
CurveKey next;
for (int i = 1; i < this._keys.Count; ++i)
{
next = this.Keys[i];
if (next.Position >= position)
{
if (prev.Continuity == CurveContinuity.Step)
{
if (position >= 1f)
{
return next.Value;
}
return prev.Value;
}
float t = (position - prev.Position) / (next.Position - prev.Position);//to have t in [0,1]
float ts = t * t;
float tss = ts * t;
//After a lot of search on internet I have found all about spline function
// and bezier (phi'sss ancien) but finaly use hermite curve
//http://en.wikipedia.org/wiki/Cubic_Hermite_spline
//P(t) = (2*t^3 - 3t^2 + 1)*P0 + (t^3 - 2t^2 + t)m0 + (-2t^3 + 3t^2)P1 + (t^3-t^2)m1
//with P0.value = prev.value , m0 = prev.tangentOut, P1= next.value, m1 = next.TangentIn
return (2 * tss - 3 * ts + 1f) * prev.Value + (tss - 2 * ts + t) * prev.TangentOut + (3 * ts - 2 * tss) * next.Value + (tss - ts) * next.TangentIn;
}
prev = next;
}
return 0f;
}
#endregion
}
}