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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 | #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 Statementsusing System;using System.Collections.Generic;using System.ComponentModel;using System.Diagnostics;using Microsoft.Xna.Framework.Design;#endregionnamespace Microsoft.Xna.Framework{ /// <summary> /// Describes a sphere in 3D-space for bounding operations. /// </summary> [Serializable] [TypeConverter(typeof(BoundingSphereConverter))] [DebuggerDisplay("{DebugDisplayString,nq}")] public struct BoundingSphere : IEquatable<BoundingSphere> { #region Internal Properties internal string DebugDisplayString { get { return string.Concat( "Center( ", Center.DebugDisplayString, " ) \r\n", "Radius( ", Radius.ToString(), " ) " ); } } #endregion #region Public Fields /// <summary> /// The sphere center. /// </summary> public Vector3 Center; /// <summary> /// The sphere radius. /// </summary> public float Radius; #endregion #region Public Constructors /// <summary> /// Constructs a bounding sphere with the specified center and radius. /// </summary> /// <param name="center">The sphere center.</param> /// <param name="radius">The sphere radius.</param> public BoundingSphere(Vector3 center, float radius) { this.Center = center; this.Radius = radius; } #endregion #region Public Methods /// <summary> /// Creates a new <see cref="BoundingSphere"/> that contains a transformation of translation and scale from this sphere by the specified <see cref="Matrix"/>. /// </summary> /// <param name="matrix">The transformation <see cref="Matrix"/>.</param> /// <returns>Transformed <see cref="BoundingSphere"/>.</returns> public BoundingSphere Transform(Matrix matrix) { BoundingSphere sphere = new BoundingSphere(); sphere.Center = Vector3.Transform(this.Center, matrix); sphere.Radius = this.Radius * ( (float) Math.Sqrt((double) Math.Max( ((matrix.M11 * matrix.M11) + (matrix.M12 * matrix.M12)) + (matrix.M13 * matrix.M13), Math.Max( ((matrix.M21 * matrix.M21) + (matrix.M22 * matrix.M22)) + (matrix.M23 * matrix.M23), ((matrix.M31 * matrix.M31) + (matrix.M32 * matrix.M32)) + (matrix.M33 * matrix.M33)) ) ) ); return sphere; } /// <summary> /// Creates a new <see cref="BoundingSphere"/> that contains a transformation of translation and scale from this sphere by the specified <see cref="Matrix"/>. /// </summary> /// <param name="matrix">The transformation <see cref="Matrix"/>.</param> /// <param name="result">Transformed <see cref="BoundingSphere"/> as an output parameter.</param> public void Transform(ref Matrix matrix, out BoundingSphere result) { result.Center = Vector3.Transform(this.Center, matrix); result.Radius = this.Radius * ( (float) Math.Sqrt((double) Math.Max( ((matrix.M11 * matrix.M11) + (matrix.M12 * matrix.M12)) + (matrix.M13 * matrix.M13), Math.Max( ((matrix.M21 * matrix.M21) + (matrix.M22 * matrix.M22)) + (matrix.M23 * matrix.M23), ((matrix.M31 * matrix.M31) + (matrix.M32 * matrix.M32)) + (matrix.M33 * matrix.M33)) ) ) ); } /// <summary> /// Test if a bounding box is fully inside, outside, or just intersecting the sphere. /// </summary> /// <param name="box">The box for testing.</param> /// <param name="result">The containment type as an output parameter.</param> public void Contains(ref BoundingBox box, out ContainmentType result) { result = this.Contains(box); } /// <summary> /// Test if a sphere is fully inside, outside, or just intersecting the sphere. /// </summary> /// <param name="sphere">The other sphere for testing.</param> /// <param name="result">The containment type as an output parameter.</param> public void Contains(ref BoundingSphere sphere, out ContainmentType result) { result = Contains(sphere); } /// <summary> /// Test if a point is fully inside, outside, or just intersecting the sphere. /// </summary> /// <param name="point">The vector in 3D-space for testing.</param> /// <param name="result">The containment type as an output parameter.</param> public void Contains(ref Vector3 point, out ContainmentType result) { result = Contains(point); } /// <summary> /// Test if a bounding box is fully inside, outside, or just intersecting the sphere. /// </summary> /// <param name="box">The box for testing.</param> /// <returns>The containment type.</returns> public ContainmentType Contains(BoundingBox box) { // Check if all corners are in sphere. bool inside = true; foreach (Vector3 corner in box.GetCorners()) { if (this.Contains(corner) == ContainmentType.Disjoint) { inside = false; break; } } if (inside) { return ContainmentType.Contains; } // Check if the distance from sphere center to cube face is less than radius. double dmin = 0; if (Center.X < box.Min.X) { dmin += (Center.X - box.Min.X) * (Center.X - box.Min.X); } else if (Center.X > box.Max.X) { dmin += (Center.X - box.Max.X) * (Center.X - box.Max.X); } if (Center.Y < box.Min.Y) { dmin += (Center.Y - box.Min.Y) * (Center.Y - box.Min.Y); } else if (Center.Y > box.Max.Y) { dmin += (Center.Y - box.Max.Y) * (Center.Y - box.Max.Y); } if (Center.Z < box.Min.Z) { dmin += (Center.Z - box.Min.Z) * (Center.Z - box.Min.Z); } else if (Center.Z > box.Max.Z) { dmin += (Center.Z - box.Max.Z) * (Center.Z - box.Max.Z); } if (dmin <= Radius * Radius) { return ContainmentType.Intersects; } // Else disjoint return ContainmentType.Disjoint; } /// <summary> /// Test if a frustum is fully inside, outside, or just intersecting the sphere. /// </summary> /// <param name="box">The box for testing.</param> /// <param name="result">The containment type as an output parameter.</param> public ContainmentType Contains(BoundingFrustum frustum) { // Check if all corners are in sphere. bool inside = true; Vector3[] corners = frustum.GetCorners(); foreach (Vector3 corner in corners) { if (this.Contains(corner) == ContainmentType.Disjoint) { inside = false; break; } } if (inside) { return ContainmentType.Contains; } // Check if the distance from sphere center to frustrum face is less than radius. double dmin = 0; // TODO : calcul dmin if (dmin <= Radius * Radius) { return ContainmentType.Intersects; } // Else disjoint return ContainmentType.Disjoint; } /// <summary> /// Test if a sphere is fully inside, outside, or just intersecting the sphere. /// </summary> /// <param name="sphere">The other sphere for testing.</param> /// <returns>The containment type.</returns> public ContainmentType Contains(BoundingSphere sphere) { float sqDistance; Vector3.DistanceSquared(ref sphere.Center, ref Center, out sqDistance); if (sqDistance > (sphere.Radius + Radius) * (sphere.Radius + Radius)) { return ContainmentType.Disjoint; } else if (sqDistance <= (Radius * sphere.Radius) * (Radius - sphere.Radius)) { return ContainmentType.Contains; } return ContainmentType.Intersects; } /// <summary> /// Test if a point is fully inside, outside, or just intersecting the sphere. /// </summary> /// <param name="point">The vector in 3D-space for testing.</param> /// <returns>The containment type.</returns> public ContainmentType Contains(Vector3 point) { float sqRadius = Radius * Radius; float sqDistance; Vector3.DistanceSquared(ref point, ref Center, out sqDistance); if (sqDistance > sqRadius) { return ContainmentType.Disjoint; } else if (sqDistance < sqRadius) { return ContainmentType.Contains; } return ContainmentType.Intersects; } /// <summary> /// Compares whether current instance is equal to specified <see cref="BoundingSphere"/>. /// </summary> /// <param name="other">The <see cref="BoundingSphere"/> to compare.</param> /// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns> public bool Equals(BoundingSphere other) { return ( this.Center == other.Center && MathHelper.WithinEpsilon(this.Radius, other.Radius) ); } #endregion #region Public Static Methods /// <summary> /// Creates the smallest <see cref="BoundingSphere"/> that can contain a specified <see cref="BoundingBox"/>. /// </summary> /// <param name="box">The box to create the sphere from.</param> /// <returns>The new <see cref="BoundingSphere"/>.</returns> public static BoundingSphere CreateFromBoundingBox(BoundingBox box) { BoundingSphere result; CreateFromBoundingBox(ref box, out result); return result; } /// <summary> /// Creates the smallest <see cref="BoundingSphere"/> that can contain a specified <see cref="BoundingBox"/>. /// </summary> /// <param name="box">The box to create the sphere from.</param> /// <param name="result">The new <see cref="BoundingSphere"/> as an output parameter.</param> public static void CreateFromBoundingBox(ref BoundingBox box, out BoundingSphere result) { // Find the center of the box. Vector3 center = new Vector3( (box.Min.X + box.Max.X) / 2.0f, (box.Min.Y + box.Max.Y) / 2.0f, (box.Min.Z + box.Max.Z) / 2.0f ); // Find the distance between the center and one of the corners of the box. float radius = Vector3.Distance(center, box.Max); result = new BoundingSphere(center, radius); } /// <summary> /// Creates the smallest <see cref="BoundingSphere"/> that can contain a specified <see cref="BoundingFrustum"/>. /// </summary> /// <param name="frustum">The frustum to create the sphere from.</param> /// <returns>The new <see cref="BoundingSphere"/>.</returns> public static BoundingSphere CreateFromFrustum(BoundingFrustum frustum) { return CreateFromPoints(frustum.GetCorners()); } /// <summary> /// Creates the smallest <see cref="BoundingSphere"/> that can contain a specified list of points in 3D-space. /// </summary> /// <param name="points">List of point to create the sphere from.</param> /// <returns>The new <see cref="BoundingSphere"/>.</returns> public static BoundingSphere CreateFromPoints(IEnumerable<Vector3> points) { if (points == null) { throw new ArgumentNullException("points"); } // From "Real-Time Collision Detection" (Page 89) Vector3 minx = new Vector3(float.MaxValue, float.MaxValue, float.MaxValue); Vector3 maxx = -minx; Vector3 miny = minx; Vector3 maxy = -minx; Vector3 minz = minx; Vector3 maxz = -minx; // Find the most extreme points along the principle axis. int numPoints = 0; foreach (Vector3 pt in points) { numPoints += 1; if (pt.X < minx.X) { minx = pt; } if (pt.X > maxx.X) { maxx = pt; } if (pt.Y < miny.Y) { miny = pt; } if (pt.Y > maxy.Y) { maxy = pt; } if (pt.Z < minz.Z) { minz = pt; } if (pt.Z > maxz.Z) { maxz = pt; } } if (numPoints == 0) { throw new ArgumentException( "You should have at least one point in points." ); } float sqDistX = Vector3.DistanceSquared(maxx, minx); float sqDistY = Vector3.DistanceSquared(maxy, miny); float sqDistZ = Vector3.DistanceSquared(maxz, minz); // Pick the pair of most distant points. Vector3 min = minx; Vector3 max = maxx; if (sqDistY > sqDistX && sqDistY > sqDistZ) { max = maxy; min = miny; } if (sqDistZ > sqDistX && sqDistZ > sqDistY) { max = maxz; min = minz; } Vector3 center = (min + max) * 0.5f; float radius = Vector3.Distance(max, center); // Test every point and expand the sphere. // The current bounding sphere is just a good approximation and may not enclose all points. // From: Mathematics for 3D Game Programming and Computer Graphics, Eric Lengyel, Third Edition. // Page 218 float sqRadius = radius * radius; foreach (Vector3 pt in points) { Vector3 diff = (pt - center); float sqDist = diff.LengthSquared(); if (sqDist > sqRadius) { float distance = (float) Math.Sqrt(sqDist); // equal to diff.Length(); Vector3 direction = diff / distance; Vector3 G = center - radius * direction; center = (G + pt) / 2; radius = Vector3.Distance(pt, center); sqRadius = radius * radius; } } return new BoundingSphere(center, radius); } /// <summary> /// Creates the smallest <see cref="BoundingSphere"/> that can contain two spheres. /// </summary> /// <param name="original">First sphere.</param> /// <param name="additional">Second sphere.</param> /// <returns>The new <see cref="BoundingSphere"/>.</returns> public static BoundingSphere CreateMerged(BoundingSphere original, BoundingSphere additional) { BoundingSphere result; CreateMerged(ref original, ref additional, out result); return result; } /// <summary> /// Creates the smallest <see cref="BoundingSphere"/> that can contain two spheres. /// </summary> /// <param name="original">First sphere.</param> /// <param name="additional">Second sphere.</param> /// <param name="result">The new <see cref="BoundingSphere"/> as an output parameter.</param> public static void CreateMerged( ref BoundingSphere original, ref BoundingSphere additional, out BoundingSphere result ) { Vector3 ocenterToaCenter = Vector3.Subtract(additional.Center, original.Center); float distance = ocenterToaCenter.Length(); // Intersect if (distance <= original.Radius + additional.Radius) { // Original contains additional. if (distance <= original.Radius - additional.Radius) { result = original; return; } // Additional contains original. if (distance <= additional.Radius - original.Radius) { result = additional; return; } } // Else find center of new sphere and radius float leftRadius = Math.Max(original.Radius - distance, additional.Radius); float Rightradius = Math.Max(original.Radius + distance, additional.Radius); // oCenterToResultCenter ocenterToaCenter = ocenterToaCenter + ( ((leftRadius - Rightradius) / (2 * ocenterToaCenter.Length())) * ocenterToaCenter ); result = new BoundingSphere(); result.Center = original.Center + ocenterToaCenter; result.Radius = (leftRadius + Rightradius) / 2; } /// <summary> /// Gets whether or not a specified <see cref="BoundingBox"/> intersects with this sphere. /// </summary> /// <param name="box">The box for testing.</param> /// <returns><c>true</c> if <see cref="BoundingBox"/> intersects with this sphere; <c>false</c> otherwise.</returns> public bool Intersects(BoundingBox box) { return box.Intersects(this); } /// <summary> /// Gets whether or not a specified <see cref="BoundingBox"/> intersects with this sphere. /// </summary> /// <param name="box">The box for testing.</param> /// <param name="result"><c>true</c> if <see cref="BoundingBox"/> intersects with this sphere; <c>false</c> otherwise. As an output parameter.</param> public void Intersects(ref BoundingBox box, out bool result) { box.Intersects(ref this, out result); } public bool Intersects(BoundingFrustum frustum) { return frustum.Intersects(this); } /// <summary> /// Gets whether or not the other <see cref="BoundingSphere"/> intersects with this sphere. /// </summary> /// <param name="sphere">The other sphere for testing.</param> /// <returns><c>true</c> if other <see cref="BoundingSphere"/> intersects with this sphere; <c>false</c> otherwise.</returns> public bool Intersects(BoundingSphere sphere) { bool result; Intersects(ref sphere, out result); return result; } /// <summary> /// Gets whether or not the other <see cref="BoundingSphere"/> intersects with this sphere. /// </summary> /// <param name="sphere">The other sphere for testing.</param> /// <param name="result"><c>true</c> if other <see cref="BoundingSphere"/> intersects with this sphere; <c>false</c> otherwise. As an output parameter.</param> public void Intersects(ref BoundingSphere sphere, out bool result) { float sqDistance; Vector3.DistanceSquared(ref sphere.Center, ref Center, out sqDistance); result = !(sqDistance > (sphere.Radius + Radius) * (sphere.Radius + Radius)); } /// <summary> /// Gets whether or not a specified <see cref="Ray"/> intersects with this sphere. /// </summary> /// <param name="ray">The ray for testing.</param> /// <returns>Distance of ray intersection or <c>null</c> if there is no intersection.</returns> public float? Intersects(Ray ray) { return ray.Intersects(this); } /// <summary> /// Gets whether or not a specified <see cref="Ray"/> intersects with this sphere. /// </summary> /// <param name="ray">The ray for testing.</param> /// <param name="result">Distance of ray intersection or <c>null</c> if there is no intersection as an output parameter.</param> public void Intersects(ref Ray ray, out float? result) { ray.Intersects(ref this, out result); } /// <summary> /// Gets whether or not a specified <see cref="Plane"/> intersects with this sphere. /// </summary> /// <param name="plane">The plane for testing.</param> /// <returns>Type of intersection.</returns> public PlaneIntersectionType Intersects(Plane plane) { PlaneIntersectionType result = default(PlaneIntersectionType); // TODO: We might want to inline this for performance reasons. this.Intersects(ref plane, out result); return result; } /// <summary> /// Gets whether or not a specified <see cref="Plane"/> intersects with this sphere. /// </summary> /// <param name="plane">The plane for testing.</param> /// <param name="result">Type of intersection as an output parameter.</param> public void Intersects(ref Plane plane, out PlaneIntersectionType result) { float distance = default(float); // TODO: We might want to inline this for performance reasons. Vector3.Dot(ref plane.Normal, ref this.Center, out distance); distance += plane.D; if (distance > this.Radius) { result = PlaneIntersectionType.Front; } else if (distance < -this.Radius) { result = PlaneIntersectionType.Back; } else { result = PlaneIntersectionType.Intersecting; } } #endregion #region Public Static Operators and Override Methods /// <summary> /// Compares whether current instance is equal to specified <see cref="Object"/>. /// </summary> /// <param name="obj">The <see cref="Object"/> to compare.</param> /// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns> public override bool Equals(object obj) { if (obj is BoundingSphere) { return this.Equals((BoundingSphere)obj); } return false; } /// <summary> /// Gets the hash code of this <see cref="BoundingSphere"/>. /// </summary> /// <returns>Hash code of this <see cref="BoundingSphere"/>.</returns> public override int GetHashCode() { return this.Center.GetHashCode() + this.Radius.GetHashCode(); } /// <summary> /// Returns a <see cref="String"/> representation of this <see cref="BoundingSphere"/> in the format: /// {Center:[<see cref="Center"/>] Radius:[<see cref="Radius"/>]} /// </summary> /// <returns>A <see cref="String"/> representation of this <see cref="BoundingSphere"/>.</returns> public override string ToString() { return ( "{Center:" + Center.ToString() + " Radius:" + Radius.ToString() + "}" ); } /// <summary> /// Compares whether two <see cref="BoundingSphere"/> instances are equal. /// </summary> /// <param name="a"><see cref="BoundingSphere"/> instance on the left of the equal sign.</param> /// <param name="b"><see cref="BoundingSphere"/> instance on the right of the equal sign.</param> /// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns> public static bool operator ==(BoundingSphere a, BoundingSphere b) { return a.Equals(b); } /// <summary> /// Compares whether two <see cref="BoundingSphere"/> instances are not equal. /// </summary> /// <param name="a"><see cref="BoundingSphere"/> instance on the left of the not equal sign.</param> /// <param name="b"><see cref="BoundingSphere"/> instance on the right of the not equal sign.</param> /// <returns><c>true</c> if the instances are not equal; <c>false</c> otherwise.</returns> public static bool operator !=(BoundingSphere a, BoundingSphere b) { return !a.Equals(b); } #endregion }} |
