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See monoxna.LICENSE for details. */ #endregion #region Using Statements using System; using System.Collections.Generic; using System.ComponentModel; using System.Diagnostics; using Microsoft.Xna.Framework.Design; #endregion namespace 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 } } |