public static bool IsOnSamePlane(GeoPointsArray3 points, ref GeoPlane plane)
{
if (points.Size() < 4)
{
return(true);
}
int count = points.Size();
int i = 2;
Vector3 p = points[0];
for (; i < count; ++i)
{
p = points[i];
if (!GeoLineUtils.IsPointInLine3(points[0], points[1], ref p))
{
break;
}
}
if (i == count)
{
return(true);
}
plane = GeoPlaneUtils.CreateFromTriangle(points[0], points[1], p);
i = 2;
int c = 2;
for (; i < count; ++i)
{
if (GeoPlaneUtils.IsPointOnPlane(plane.mNormal, plane.mD, points[i]))
{
c++;
}
}
return(c == count);
}
public static List <Vector3> PlaneTransformGlobal(List <Vector2> ps, GeoPlane plane)
{
List <Vector3> tmp = new List <Vector3>();
foreach (Vector3 p in ps)
{
Vector3 v = new Vector3(p.x, 0.0f, p.y);
tmp.Add(plane.TransformToGlobal(v));
}
return(tmp);
}
public static List <Vector2> PlaneTransformLocal(List <Vector3> ps, GeoPlane plane)
{
List <Vector2> tmp = new List <Vector2>();
foreach (Vector3 p in ps)
{
Vector3 p1 = plane.TransformToLocal(p);
tmp.Add(new Vector2(p1.x, p1.z));
}
return(tmp);
}
public QHullTrianglePlane(Vector3 a, Vector3 b)
{
Vector3 normal = Vector3.Cross(b - a, Vector3.forward);
normal.Normalize();
float d = -Vector3.Dot(normal, a);
mPlane = new GeoPlane(normal, d);
mVertexPoints = new Vector3[3];
mVertexPoints[0] = a;
mVertexPoints[1] = b;
mVertexPoints[2] = Vector3.zero;
}
public static bool IsTriangleInsectSphere(Vector3 p1, Vector3 p2, Vector3 p3, Vector3 center, float r, ref GeoInsectPointArrayInfo insect)
{
GeoPlane plane = GeoPlaneUtils.CreateFromTriangle(p1, p2, p3);
bool isInsec = GeoPlaneUtils.IsPlaneInsectSphere(plane, center, r, ref insect);
if (isInsec)
{
Vector3 c1 = insect.mHitGlobalPoint.mPointArray[0];
float rad = insect.mHitGlobalPoint.mPointArray[0][0];
insect.Clear();
return(IsTriangleInsectPlaneCircle2(p1, p2, p3, c1, rad, plane, ref insect));
}
return(false);
}
public static float PointClosest2Triangle3(Vector3 p1, Vector3 p2, Vector3 p3, ref Vector3 p, ref Vector3 close)
{
GeoPlane plane = new GeoPlane(p1, p2, p3);
float d = GeoPlaneUtils.PointClosestToPlaneAbs(plane.mNormal, plane.mD, p, ref close);
if (GeoTriangleUtils.IsPointInTriangle3(p1, p2, p3, ref close))
{
return(d);
}
else
{
Vector3 close1 = new Vector3();
float dt = PointClosest2PlaneTriangle2(p1, p2, p3, plane, ref p, ref close1);
return((float)Math.Sqrt(d * d + dt * dt));
}
}
public static bool IsAABBInsectTriangle2Plane(Vector3 min, Vector3 max, GeoPlane plane, Vector3 p1, Vector3 p2, Vector3 p3, ref GeoInsectPointArrayInfo insect)
{
Vector2 p11, p21, p31;
GeoPlaneUtils.PlaneTransformLocalTriangle(p1, p2, p3, plane, out p11, out p21, out p31);
Vector3 vmin = plane.TransformToLocal(min);
Vector3 vmax = plane.TransformToLocal(max);
bool isInsect = IsAABBInsectTriangle2(vmin, vmax, p11, p21, p31, ref insect);
if (isInsect)
{
insect.mIsIntersect = true;
insect.mHitGlobalPoint.mPointArray = GeoPlaneUtils.PlaneTransformGlobal(insect.mHitGlobalPoint.mPointArray, plane);
}
return(insect.mIsIntersect);
}
public static bool IsPlaneInsectSphere(GeoPlane plane, Vector3 center, float r, ref GeoInsectPointArrayInfo insect)
{
Vector3 close = new Vector3();
float dist = PointClosestToPlaneAbs(plane.mNormal, plane.mD, center, ref close);
if (dist > r)
{
return(false);
}
float rad = Mathf.Sqrt(r * r - dist * dist);
insect.mIsIntersect = true;
insect.mHitGlobalPoint.mPointArray.Add(close);
insect.mHitGlobalPoint.mPointArray.Add(Vector3.one * rad); // 相交为一个圆，所在平明为 plane
return(true);
}
public static GeoPointsArray3 BuildConvexHull(GeoPointsArray3 points)
{
points.Distinct();
GeoPlane plane = new GeoPlane(Vector3.zero, 0);
if (IsOnSamePlane(points, ref plane))
{
GeoPointsArray2 point2 = new GeoPointsArray2(GeoPlaneUtils.PlaneTransformLocal(points.mPointArray, plane));
point2 = BuildConvexHull(point2);
return(new GeoPointsArray3(GeoPlaneUtils.PlaneTransformGlobal(point2.mPointArray, plane)));
}
else
{
return(new GeoPointsArray3(QuickHull.BuildHull(points)));
}
}
public static float PointClosest2PlaneAABB2(Vector3 min, Vector3 max, GeoPlane plane, ref Vector3 p, ref Vector3 close1)
{
Vector3 min1 = plane.TransformToLocal(min);
Vector3 max1 = plane.TransformToLocal(max);
Vector3 p1 = plane.TransformToLocal(p);
Vector2 min2 = new Vector2(min1.x, min1.z);
Vector2 max2 = new Vector2(max1.x, max1.z);
Vector2 p2 = new Vector2(p1.x, p1.z);
Vector2 close = new Vector2();
float temp = PointClosest2AABB2(min2, max2, ref p2, ref close);
if (p1.y != 0)
{
temp = Mathf.Sqrt(temp * temp + p1.y * p1.y);
}
p1 = new Vector3(close.x, 0.0f, close.y);
close1 = plane.TransformToGlobal(p1);
return(temp);
}
public static bool IsPointInAABB2Plane(Vector3 min, Vector3 max, GeoPlane plane, ref Vector3 p)
{
if (!GeoPlaneUtils.IsPointOnPlane(plane.mNormal, plane.mD, p))
{
return(false);
}
Vector3 size = max - min;
float sx = Vector3.Dot(size, plane.mAxisX);
float sz = Vector3.Dot(size, plane.mAxisZ);
Vector3 pc = p - min;
float d1 = Vector3.Dot(pc, plane.mAxisX);
float d2 = Vector3.Dot(pc, plane.mAxisZ);
if (d1 < sx && d2 < sz)
{
return(true);
}
return(false);
}
// 两三角面 共面的情况
private static bool IsTriangleInsectTrianglePlane2(Vector3 p1, Vector3 p2, Vector3 p3, Vector3 p4, Vector3 p5, Vector3 p6, ref GeoInsectPointArrayInfo insect)
{
GeoPlane plane = GeoPlaneUtils.CreateFromTriangle(p1, p2, p3);
Vector2 p11, p21, p31, p41, p51, p61;
GeoPlaneUtils.PlaneTransformLocalTriangle(p1, p2, p3, plane, out p11, out p21, out p31);
GeoPlaneUtils.PlaneTransformLocalTriangle(p4, p5, p6, plane, out p41, out p51, out p61);
GeoInsectPointArrayInfo tmp = new GeoInsectPointArrayInfo();
bool isInsect = IsTriangleInsectTriangle2(p11, p21, p31, p41, p51, p61, ref tmp);
if (isInsect)
{
foreach (Vector3 v in tmp.mHitGlobalPoint.mPointArray)
{
Vector3 vt = new Vector3(v.x, 0.0f, v.z);
vt = plane.TransformToGlobal(vt);
insect.mHitGlobalPoint.mPointArray.Add(vt);
}
insect.mIsIntersect = insect.mHitGlobalPoint.mPointArray.Count > 0;
}
return(insect.mIsIntersect);
}
public static bool IsCircleInsectCircle3(Vector3 center1, float r1, GeoPlane plane1, Vector3 center2, float r2, GeoPlane plane2, ref GeoInsectPointArrayInfo insect)
{
float dot = Mathf.Abs(Vector3.Dot(plane1.mNormal, plane2.mNormal));
if (1 - dot < 1e-5f)
{
if (GeoPlaneUtils.IsPointOnPlane(plane2.mNormal, plane2.mD, center1)) // 共面
{
return(IsCircleInsectCirclePlane2(center1, r1, center2, r2, plane2, ref insect));
}
return(false);
}
GeoInsectPointArrayInfo tmp = new GeoInsectPointArrayInfo();
bool isInsect = GeoPlaneUtils.IsPlaneInsectCircle(plane1.mNormal, plane1.mD, center2, r2, plane2, ref tmp);
if (isInsect)
{
Vector3 lin1 = tmp.mHitGlobalPoint.mPointArray[0];
Vector3 lin2 = lin1 + tmp.mHitGlobalPoint.mPointArray[1];
GeoLineUtils.IsLineInsectCirclePlane2(lin1, lin2, center1, r1, plane1, ref insect);
}
return(insect.mIsIntersect);
}
public static bool IsAABBInsectCircle3(Vector3 min, Vector3 max, GeoPlane plane1, Vector3 center, float r, GeoPlane plane2, ref GeoInsectPointArrayInfo insect)
{
float dot = Vector3.Dot(plane1.mNormal, plane2.mNormal);
if (1 - Mathf.Abs(dot) < 1e-5f)
{
if (GeoPlaneUtils.IsPointOnPlane(plane2.mNormal, plane2.mD, min))
{
return(IsAABBInsectCirclePlane2(min, max, center, r, plane1, ref insect)); // should use plane1
}
return(false);
}
GeoInsectPointArrayInfo tmp = new GeoInsectPointArrayInfo();
bool isInsect = GeoPlaneUtils.IsPlaneInsectCircle(plane1.mNormal, plane1.mD, center, r, plane2, ref tmp);
if (isInsect)
{
if (tmp.mHitGlobalPoint.mPointArray.Count == 1)
{
Vector3 line1 = tmp.mHitGlobalPoint.mPointArray[0];
if (GeoAABBUtils.IsPointInAABB2Plane(min, max, plane1, ref line1))
{
insect.mIsIntersect = true;
insect.mHitGlobalPoint.mPointArray.Add(line1);
return(true);
}
}
else
{
Vector3 seg1 = tmp.mHitGlobalPoint.mPointArray[0];
Vector3 seg2 = seg1 + tmp.mHitGlobalPoint.mPointArray[1];
return(GeoSegmentUtils.IsSegmentInsectAABB2Plane(seg1, seg2, min, max, plane1, ref insect));
}
}
return(false);
}
public static bool IsRayInsectCircle3(Vector3 rayOrigin, Vector3 rayDirection, Vector3 center, float r, GeoPlane plane, ref GeoInsectPointInfo insect)
{
if (GeoPlaneUtils.IsPlaneInsectRay(plane.mNormal, plane.mD, rayOrigin, rayDirection, ref insect))
{
if (GeoCircleUtils.IsInSphere(center, r, insect.mHitGlobalPoint))
{
return(true);
}
}
return(false);
}
public static bool IsAABBInsectCirclePlane2(Vector3 min, Vector3 max, Vector3 center, float r, GeoPlane plane, ref GeoInsectPointArrayInfo insect)
{
Vector3 min1 = plane.TransformToLocal(min);
Vector3 max1 = plane.TransformToLocal(max);
Vector3 c1 = plane.TransformToLocal(center);
bool isInsect = IsAABBInsectCircle2(min1, max1, c1, r, ref insect);
if (isInsect)
{
insect.mHitGlobalPoint.mPointArray = GeoPlaneUtils.PlaneTransformGlobal(insect.mHitGlobalPoint.mPointArray, plane);
}
return(isInsect);
}
public static void PlaneTransformGlobaleTriangle(Vector3 p1, Vector3 p2, Vector3 p3, GeoPlane plane, out Vector2 p11, out Vector2 p21, out Vector2 p31)
{
Vector3 p1t = plane.TransformToGlobal(p1);
Vector3 p2t = plane.TransformToGlobal(p2);
Vector3 p3t = plane.TransformToGlobal(p3);
p11 = new Vector2(p1t.x, p1t.z);
p21 = new Vector2(p2t.x, p2t.z);
p31 = new Vector2(p3t.x, p3t.z);
}
public static void PlaneTransformGlobaleTriangle(Vector3 p1, Vector3 p2, Vector3 p3, GeoPlane plane, out Vector3 p11, out Vector3 p21, out Vector3 p31)
{
p11 = plane.TransformToGlobal(p1);
p21 = plane.TransformToGlobal(p2);
p31 = plane.TransformToGlobal(p3);
}
public static bool IsPlaneInsectAABB2(Vector3 normal, float d, Vector3 min, Vector3 max, GeoPlane plane, ref GeoInsectPointArrayInfo insect)
{
float dot = Vector3.Dot(normal, plane.mNormal);
if (1 - Mathf.Abs(dot) < 1e-5f)
{
return(false);
}
GeoInsectPointArrayInfo tmp = new GeoInsectPointArrayInfo();
bool isInsect = GeoPlaneUtils.IsPlaneInsectPlane(normal, d, plane.mNormal, plane.mD, ref tmp);
if (isInsect)
{
Vector3 l1 = tmp.mHitGlobalPoint.mPointArray[0];
Vector3 l2 = l1 + tmp.mHitGlobalPoint.mPointArray[1];
isInsect = GeoLineUtils.IsLineInsectAABBPlane2(l1, l2, min, max, plane, ref insect);
}
return(insect.mIsIntersect);
}
public static bool IsTriangleInsectCircle3(Vector3 p1, Vector3 p2, Vector3 p3, Vector3 center, float r, GeoPlane plane, ref GeoInsectPointArrayInfo insect)
{
bool isInsect = GeoPlaneUtils.IsPlaneInsectTriangle(plane.mNormal, plane.mD, p1, p2, p3, ref insect);
if (isInsect)
{
if (insect.mHitGlobalPoint.mPointArray.Count == 3) // 共面， 转化成 2d
{
insect.Clear();
return(IsTriangleInsectPlaneCircle2(p1, p2, p3, center, r, plane, ref insect));
}
else if (insect.mHitGlobalPoint.mPointArray.Count == 1)
{
if (GeoCircleUtils.IsInSphere(center, r, insect.mHitGlobalPoint.mPointArray[0]))
{
return(true);
}
}
else if (insect.mHitGlobalPoint.mPointArray.Count == 2)
{
Vector3 seg1 = plane.TransformToLocal(insect.mHitGlobalPoint.mPointArray[0]);
Vector3 seg2 = plane.TransformToLocal(insect.mHitGlobalPoint.mPointArray[1]);
Vector3 c1 = plane.TransformToLocal(center);
Vector2 p12 = new Vector2(seg1.x, seg1.z);
Vector2 p22 = new Vector2(seg2.x, seg2.z);
Vector2 c2 = new Vector2(c1.x, c1.z);
insect.Clear();
GeoInsectPointArrayInfo temp = new GeoInsectPointArrayInfo();
if (GeoSegmentUtils.IsSegmentInsectCircle2(p12, p22, c2, r, ref temp))
{
insect.mIsIntersect = true;
foreach (Vector3 v in temp.mHitGlobalPoint.mPointArray)
{
Vector3 vv = new Vector3(v.x, 0.0f, v.y);
vv = plane.TransformToGlobal(vv);
insect.mHitGlobalPoint.mPointArray.Add(vv);
}
return(true);
}
}
}
return(false);
}
public static bool IsLineInsectAABBPlane2(Vector3 line1, Vector3 line2, Vector3 min, Vector3 max, GeoPlane plane, ref GeoInsectPointArrayInfo insect)
{
Vector3 min1 = plane.TransformToLocal(min);
Vector3 max1 = plane.TransformToLocal(max);
Vector3 l1 = plane.TransformToLocal(line1);
Vector3 l2 = plane.TransformToLocal(line2);
bool isInsect = IsLineInsectAABB2(new Vector2(l1.x, l1.z), new Vector2(l2.x, l2.z), new Vector2(min1.x, min1.z), new Vector2(max1.x, max1.z), ref insect);
if (isInsect)
{
insect.mHitGlobalPoint.mPointArray = GeoPlaneUtils.PlaneTransformGlobal(insect.mHitGlobalPoint.mPointArray, plane);
}
return(isInsect);
}
public static bool IsSegmentInsectCircle3(Vector3 seg1, Vector3 seg2, Vector3 center, float r, GeoPlane plane, ref GeoInsectPointInfo insect)
{
bool isInsect = GeoPlaneUtils.IsPlaneInsectSegment(plane.mNormal, plane.mD, seg1, seg2, ref insect);
if (isInsect)
{
if (GeoCircleUtils.IsInSphere(center, r, insect.mHitGlobalPoint))
{
return(true);
}
}
insect.mIsIntersect = isInsect;
return(isInsect);
}
public static bool IsTriangleInsectPlaneCircle2(Vector3 p1, Vector3 p2, Vector3 p3, Vector3 center, float r, GeoPlane plane, ref GeoInsectPointArrayInfo insect)
{
Vector3 p11 = plane.TransformToLocal(p1);
Vector3 p21 = plane.TransformToLocal(p2);
Vector3 p31 = plane.TransformToLocal(p3);
Vector3 c1 = plane.TransformToLocal(center);
Vector2 p12 = new Vector2(p11.x, p11.z);
Vector2 p22 = new Vector2(p21.x, p21.z);
Vector2 p32 = new Vector2(p31.x, p31.z);
Vector2 c2 = new Vector2(c1.x, c1.z);
GeoInsectPointArrayInfo temp = new GeoInsectPointArrayInfo();
bool isInsect1 = IsTriangleInsectCircle2(p12, p22, p32, c2, r, ref temp);
if (isInsect1)
{
insect.mIsIntersect = true;
foreach (Vector3 v in temp.mHitGlobalPoint.mPointArray)
{
Vector3 vv = new Vector3(v.x, 0.0f, v.y);
vv = plane.TransformToGlobal(vv);
insect.mHitGlobalPoint.mPointArray.Add(vv);
}
return(true);
}
return(false);
}
public static float PointClosest2PlaneTriangle2(Vector3 p1, Vector3 p2, Vector3 p3, GeoPlane plane, ref Vector3 p, ref Vector3 close)
{
Vector2 p11, p21, p31, pt;
GeoPlaneUtils.PlaneTransformLocalTriangle(p1, p2, p3, plane, out p11, out p21, out p31);
Vector3 pp = plane.TransformToLocal(p);
pt = new Vector2(pp.x, pp.z);
Vector2 close1 = new Vector2();
float d = PointClosest2Triangle2(p11, p21, p31, ref pt, ref close1);
close.x = close1.x;
close.y = 0;
close.z = close1.y;
close = plane.TransformToGlobal(close);
return(d);
}
public static bool IsSegmentInsectAABB2Plane(Vector3 seg1, Vector3 seg2, Vector3 min, Vector2 max, GeoPlane plane, ref GeoInsectPointArrayInfo insect)
{
Vector3 s1 = plane.TransformToLocal(seg1);
Vector3 s2 = plane.TransformToLocal(seg2);
Vector3 min1 = plane.TransformToLocal(min);
Vector3 max1 = plane.TransformToLocal(max);
bool isInsect = IsSegmentInsectAABB2(s1, s2, min1, max1, ref insect);
if (isInsect)
{
insect.mHitGlobalPoint.mPointArray = GeoPlaneUtils.PlaneTransformGlobal(insect.mHitGlobalPoint.mPointArray, plane);
}
return(isInsect);
}
public static bool IsLineInsectCirclePlane2(Vector3 line1, Vector3 line2, Vector3 center, float r, GeoPlane plane, ref GeoInsectPointArrayInfo insect)
{
Vector3 l1 = plane.TransformToLocal(line1);
Vector3 l2 = plane.TransformToLocal(line2);
Vector3 c1 = plane.TransformToLocal(center);
bool isInsect = IsLineInsectCircle2(new Vector2(l1.x, l1.z), new Vector2(l2.x, l2.z), new Vector2(c1.x, c1.z), r, ref insect);
if (isInsect)
{
insect.mHitGlobalPoint.mPointArray = GeoPlaneUtils.PlaneTransformGlobal(insect.mHitGlobalPoint.mPointArray, plane);
}
return(insect.mIsIntersect);
}
public static float PointDistanceToPlane(GeoPlane plane, Vector3 p)
{
return(PointDistanceToPlane(plane.mNormal, plane.mD, p));
}
public static bool IsPlaneInsectCircle(Vector3 normal, float d, Vector3 center, float r, GeoPlane plane, ref GeoInsectPointArrayInfo insect)
{
float tmp = Mathf.Abs(Vector3.Dot(plane.mNormal.normalized, normal.normalized));
if (1 - tmp < 1e-5f)
{
return(false); // 平行 或 共面
}
GeoInsectPointArrayInfo tmp1 = new GeoInsectPointArrayInfo();
bool inSect = IsPlaneInsectPlane(normal, d, plane.mNormal, plane.mD, ref tmp1);
if (inSect)
{
Vector3 line1 = tmp1.mHitGlobalPoint.mPointArray[0] + tmp1.mHitGlobalPoint.mPointArray[1];
GeoLineUtils.IsLineInsectCirclePlane2(tmp1.mHitGlobalPoint.mPointArray[0], line1, center, r, plane, ref insect);
}
return(insect.mIsIntersect);
}
public static bool IsPointInPositiveHalf(GeoPlane plane, Vector3 p)
{
float d = PointDistanceToPlane(plane, p);
return(d > 1e-5f);
}
public static bool IsLineInsectCircle3(Vector3 line1, Vector3 line2, Vector3 center, float r, GeoPlane plane, ref GeoInsectPointArrayInfo insect)
{
if (GeoPlaneUtils.IsPointOnPlane(plane.mNormal, plane.mD, line1) && GeoPlaneUtils.IsPointOnPlane(plane.mNormal, plane.mD, line2))
{
return(IsLineInsectCirclePlane2(line1, line2, center, r, plane, ref insect));
}
GeoInsectPointInfo info = new GeoInsectPointInfo();
bool isInsect = GeoPlaneUtils.IsPlaneInsectLine(plane.mNormal, plane.mD, line1, line2, ref info);
if (isInsect)
{
if (GeoCircleUtils.IsInSphere(center, r, info.mHitGlobalPoint))
{
insect.mIsIntersect = true;
insect.mHitGlobalPoint.mPointArray.Add(info.mHitGlobalPoint);
return(true);
}
insect.mIsIntersect = false;
}
return(false);
}