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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 | #region License /* FNA - XNA4 Reimplementation for Desktop Platforms * Copyright 2009-2016 Ethan Lee and the MonoGame Team * * Released under the Microsoft Public License. * See LICENSE for details. */ /* Derived from code by the Mono.Xna Team (Copyright 2006). * Released under the MIT License. See monoxna.LICENSE for details. */ #endregion #region Using Statements using System; #endregion namespace Microsoft.Xna.Framework { /// <summary> /// Contains a collection of <see cref="CurveKey"/> points in 2D space and provides methods for evaluating features of the curve they define. /// </summary> [Serializable] public class Curve { #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 Keys.Count <= 1; } } /// <summary> /// The collection of curve keys. /// </summary> public CurveKeyCollection Keys { get ; private set ; } /// <summary> /// Defines how to handle weighting values that are greater than the last control point in the curve. /// </summary> public CurveLoopType PostLoop { get ; set ; } /// <summary> /// Defines how to handle weighting values that are less than the first control point in the curve. /// </summary> public CurveLoopType PreLoop { get ; set ; } #endregion #region Public Constructors /// <summary> /// Constructs a curve. /// </summary> public Curve() { Keys = new CurveKeyCollection(); } #endregion #region Private Constructors private Curve(CurveKeyCollection keys) { Keys = keys; } #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(Keys.Clone()); curve.PreLoop = PreLoop; curve.PostLoop = 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) { if (Keys.Count == 0) { return 0.0f; } if (Keys.Count == 1) { return Keys[0].Value; } CurveKey first = Keys[0]; CurveKey last = Keys[Keys.Count - 1]; if (position < first.Position) { switch ( this .PreLoop) { case CurveLoopType.Constant: return first.Value; case CurveLoopType.Linear: // Linear y = a*x +b with a tangent 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) { 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: return last.Value; case CurveLoopType.Linear: // Linear y = a*x +b with a tangent 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) { 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 ( int i = 0; i < Keys.Count; i += 1) { 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 ) { CurveKey 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: float pn = p1 - p0; if (MathHelper.WithinEpsilon(pn, 0.0f)) { 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: float 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 -= 1; } return ( int ) cycle; } private float GetCurvePosition( float position) { // Only for position in curve. CurveKey prev = Keys[0]; CurveKey next; for ( int i = 1; i < Keys.Count; i += 1) { next = Keys[i]; if (next.Position >= position) { if (prev.Continuity == CurveContinuity.Step) { if (position >= 1f) { return next.Value; } return prev.Value; } // To have t in [0,1] float t = ( (position - prev.Position) / (next.Position - prev.Position) ); 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 finally * used hermite curve: * 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 } } |