C++ idPlane::Normal方法代码示例

void R_LocalPlaneToGlobal( const float modelMatrix[16], const idPlane &in, idPlane &out ) {
	float	offset;

	R_LocalVectorToGlobal( modelMatrix, in.Normal(), out.Normal() );

	offset = modelMatrix[12] * out[0] + modelMatrix[13] * out[1] + modelMatrix[14] * out[2];
	out[3] = in[3] - offset;
}

/*
============
idBrush::FromWinding
============
*/
bool idBrush::FromWinding( const idWinding& w, const idPlane& windingPlane )
{
	int i, j, bestAxis;
	idPlane plane;
	idVec3 normal, axialNormal;
	
	sides.Append( new idBrushSide( windingPlane, -1 ) );
	sides.Append( new idBrushSide( -windingPlane, -1 ) );
	
	bestAxis = 0;
	for( i = 1; i < 3; i++ )
	{
		if( idMath::Fabs( windingPlane.Normal()[i] ) > idMath::Fabs( windingPlane.Normal()[bestAxis] ) )
		{
			bestAxis = i;
		}
	}
	axialNormal = vec3_origin;
	if( windingPlane.Normal()[bestAxis] > 0.0f )
	{
		axialNormal[bestAxis] = 1.0f;
	}
	else
	{
		axialNormal[bestAxis] = -1.0f;
	}
	
	for( i = 0; i < w.GetNumPoints(); i++ )
	{
		j = ( i + 1 ) % w.GetNumPoints();
		normal = ( w[j].ToVec3() - w[i].ToVec3() ).Cross( axialNormal );
		if( normal.Normalize() < 0.5f )
		{
			continue;
		}
		plane.SetNormal( normal );
		plane.FitThroughPoint( w[j].ToVec3() );
		sides.Append( new idBrushSide( plane, -1 ) );
	}
	
	if( sides.Num() < 4 )
	{
		for( i = 0; i < sides.Num(); i++ )
		{
			delete sides[i];
		}
		sides.Clear();
		return false;
	}
	
	sides[0]->winding = w.Copy();
	windingsValid = true;
	BoundBrush();
	
	return true;
}

/*
================
idBox::PlaneSide
================
*/
int idBox::PlaneSide( const idPlane &plane, const float epsilon ) const {
	float d1, d2;

	d1 = plane.Distance( center );
	d2 = idMath::Fabs( extents[0] * plane.Normal()[0] ) +
			idMath::Fabs( extents[1] * plane.Normal()[1] ) +
				idMath::Fabs( extents[2] * plane.Normal()[2] );

	if ( d1 - d2 > epsilon ) {
		return PLANESIDE_FRONT;
	}
	if ( d1 + d2 < -epsilon ) {
		return PLANESIDE_BACK;
	}
	return PLANESIDE_CROSS;
}

/*
================
idBox::PlaneDistance
================
*/
float idBox::PlaneDistance( const idPlane &plane ) const {
	float d1, d2;

	d1 = plane.Distance( center );
	d2 = idMath::Fabs( extents[0] * plane.Normal()[0] ) +
			idMath::Fabs( extents[1] * plane.Normal()[1] ) +
				idMath::Fabs( extents[2] * plane.Normal()[2] );

	if ( d1 - d2 > 0.0f ) {
		return d1 - d2;
	}
	if ( d1 + d2 < 0.0f ) {
		return d1 + d2;
	}
	return 0.0f;
}

/*
================
idBounds::PlaneSide
================
*/
int idBounds::PlaneSide( const idPlane &plane, const float epsilon ) const {
	idVec3 center;
	float d1, d2;

	center = ( b[0] + b[1] ) * 0.5f;

	d1 = plane.Distance( center );
	d2 = idMath::Fabs( ( b[1][0] - center[0] ) * plane.Normal()[0] ) +
			idMath::Fabs( ( b[1][1] - center[1] ) * plane.Normal()[1] ) +
				idMath::Fabs( ( b[1][2] - center[2] ) * plane.Normal()[2] );

	if ( d1 - d2 > epsilon ) {
		return PLANESIDE_FRONT;
	}
	if ( d1 + d2 < -epsilon ) {
		return PLANESIDE_BACK;
	}
	return PLANESIDE_CROSS;
}

/*
================
idBounds::PlaneDistance
================
*/
float idBounds::PlaneDistance( const idPlane &plane ) const {
	idVec3 center;
	float d1, d2;

	center = ( b[0] + b[1] ) * 0.5f;

	d1 = plane.Distance( center );
	d2 = idMath::Fabs( ( b[1][0] - center[0] ) * plane.Normal()[0] ) +
			idMath::Fabs( ( b[1][1] - center[1] ) * plane.Normal()[1] ) +
				idMath::Fabs( ( b[1][2] - center[2] ) * plane.Normal()[2] );

	if ( d1 - d2 > 0.0f ) {
		return d1 - d2;
	}
	if ( d1 + d2 < 0.0f ) {
		return d1 + d2;
	}
	return 0.0f;
}

/*
================
idPlane::PlaneIntersection
================
*/
bool idPlane::PlaneIntersection( const idPlane &plane, idVec3 &start, idVec3 &dir ) const {
	double n00, n01, n11, det, invDet, f0, f1;

	n00 = Normal().LengthSqr();
	n01 = Normal() * plane.Normal();
	n11 = plane.Normal().LengthSqr();
	det = n00 * n11 - n01 * n01;

	if ( idMath::Fabs(det) < 1e-6f ) {
		return false;
	}

	invDet = 1.0f / det;
	f0 = ( n01 * plane.d - n11 * d ) * invDet;
	f1 = ( n01 * d - n00 * plane.d ) * invDet;

	dir = Normal().Cross( plane.Normal() );
	start = f0 * Normal() + f1 * plane.Normal();
	return true;
}

/*
============
idAASLocal::EdgeSplitPoint

  calculates split point of the edge with the plane
  returns true if the split point is between the edge vertices
============
*/
bool idAASLocal::EdgeSplitPoint( idVec3 &split, int edgeNum, const idPlane &plane ) const {
	const aasEdge_t *edge;
	idVec3 v1, v2;
	float d1, d2;
	edge = &file->GetEdge( edgeNum );
	v1 = file->GetVertex( edge->vertexNum[0] );
	v2 = file->GetVertex( edge->vertexNum[1] );
	d1 = v1 * plane.Normal() - plane.Dist();
	d2 = v2 * plane.Normal() - plane.Dist();
	//if ( (d1 < CM_CLIP_EPSILON && d2 < CM_CLIP_EPSILON) || (d1 > -CM_CLIP_EPSILON && d2 > -CM_CLIP_EPSILON) ) {
	if( FLOATSIGNBITSET( d1 ) == FLOATSIGNBITSET( d2 ) ) {
		return false;
	}
	split = v1 + ( d1 / ( d1 - d2 ) ) * ( v2 - v1 );
	return true;
}

/*
=================
idSurface::Split
=================
*/
int idSurface::Split( const idPlane &plane, const float epsilon, idSurface **front, idSurface **back, int *frontOnPlaneEdges, int *backOnPlaneEdges ) const {
	float *			dists;
	float			f;
	byte *			sides;
	int				counts[3];
	int *			edgeSplitVertex;
	int				numEdgeSplitVertexes;
	int *			vertexRemap[2];
	int				vertexIndexNum[2][2];
	int *			vertexCopyIndex[2];
	int *			indexPtr[2];
	int				indexNum[2];
	int *			index;
	int *			onPlaneEdges[2];
	int				numOnPlaneEdges[2];
	int				maxOnPlaneEdges;
	int				i;
	idSurface *		surface[2];
	idDrawVert		v;

	dists = (float *) _alloca( verts.Num() * sizeof( float ) );
	sides = (byte *) _alloca( verts.Num() * sizeof( byte ) );

	counts[0] = counts[1] = counts[2] = 0;

	// determine side for each vertex
	for ( i = 0; i < verts.Num(); i++ ) {
		dists[i] = f = plane.Distance( verts[i].xyz );
		if ( f > epsilon ) {
			sides[i] = SIDE_FRONT;
		} else if ( f < -epsilon ) {
			sides[i] = SIDE_BACK;
		} else {
			sides[i] = SIDE_ON;
		}
		counts[sides[i]]++;
	}

	*front = *back = NULL;

	// if coplanar, put on the front side if the normals match
	if ( !counts[SIDE_FRONT] && !counts[SIDE_BACK] ) {

		f = ( verts[indexes[1]].xyz - verts[indexes[0]].xyz ).Cross( verts[indexes[0]].xyz - verts[indexes[2]].xyz ) * plane.Normal();
		if ( FLOATSIGNBITSET( f ) ) {
			*back = new idSurface( *this );
			return SIDE_BACK;
		} else {
			*front = new idSurface( *this );
			return SIDE_FRONT;
		}
	}
	// if nothing at the front of the clipping plane
	if ( !counts[SIDE_FRONT] ) {
		*back = new idSurface( *this );
		return SIDE_BACK;
	}
	// if nothing at the back of the clipping plane
	if ( !counts[SIDE_BACK] ) {
		*front = new idSurface( *this );
		return SIDE_FRONT;
	}

	// allocate front and back surface
	*front = surface[0] = new idSurface();
	*back = surface[1] = new idSurface();

	edgeSplitVertex = (int *) _alloca( edges.Num() * sizeof( int ) );
	numEdgeSplitVertexes = 0;

	maxOnPlaneEdges = 4 * counts[SIDE_ON];
	counts[SIDE_FRONT] = counts[SIDE_BACK] = counts[SIDE_ON] = 0;

	// split edges
	for ( i = 0; i < edges.Num(); i++ ) {
		int v0 = edges[i].verts[0];
		int v1 = edges[i].verts[1];
		int sidesOr = ( sides[v0] | sides[v1] );

		// if both vertexes are on the same side or one is on the clipping plane
		if ( !( sides[v0] ^ sides[v1] ) || ( sidesOr & SIDE_ON ) ) {
			edgeSplitVertex[i] = -1;
			counts[sidesOr & SIDE_BACK]++;
			counts[SIDE_ON] += ( sidesOr & SIDE_ON ) >> 1;
		} else {

/*
=============
R_ChopWinding

Clips a triangle from one buffer to another, setting edge flags
The returned buffer may be the same as inNum if no clipping is done
If entirely clipped away, clipTris[returned].numVerts == 0

I have some worries about edge flag cases when polygons are clipped
multiple times near the epsilon.
=============
*/
static int R_ChopWinding( clipTri_t clipTris[2], int inNum, const idPlane plane ) {
	clipTri_t	*in, *out;
	float	dists[MAX_CLIPPED_POINTS];
	int		sides[MAX_CLIPPED_POINTS];
	int		counts[3];
	float	dot;
	int		i, j;
	idVec3	mid;
	bool	front;

	in = &clipTris[inNum];
	out = &clipTris[inNum^1];
	counts[0] = counts[1] = counts[2] = 0;

	// determine sides for each point
	front = false;
	for ( i = 0; i < in->numVerts; i++ ) {
		dot = in->verts[i] * plane.Normal() + plane[3];
		dists[i] = dot;
		if ( dot < LIGHT_CLIP_EPSILON ) {	// slop onto the back
			sides[i] = SIDE_BACK;
		} else {
			sides[i] = SIDE_FRONT;
			if ( dot > LIGHT_CLIP_EPSILON ) {
				front = true;
			}
		}
		counts[sides[i]]++;
	}

	// if none in front, it is completely clipped away
	if ( !front ) {
		in->numVerts = 0;
		return inNum;
	}
	if ( !counts[SIDE_BACK] ) {
		return inNum;		// inout stays the same
	}

	// avoid wrapping checks by duplicating first value to end
	sides[i] = sides[0];
	dists[i] = dists[0];
	in->verts[in->numVerts] = in->verts[0];

	out->numVerts = 0;
	for ( i = 0 ; i < in->numVerts ; i++ ) {
		idVec3 &p1 = in->verts[i];
		
		if ( sides[i] == SIDE_FRONT ) {
			out->verts[out->numVerts] = p1;
			out->numVerts++;
		}

		if ( sides[i+1] == sides[i] ) {
			continue;
		}
			
		// generate a split point
		idVec3 &p2 = in->verts[i+1];
		
		dot = dists[i] / ( dists[i] - dists[i+1] );
		for ( j = 0; j < 3; j++ ) {
			mid[j] = p1[j] + dot * ( p2[j] - p1[j] );
		}
			
		out->verts[out->numVerts] = mid;

		out->numVerts++;
	}

	return inNum ^ 1;
}

//.........这里部分代码省略.........
			{
				maxBackWinding[i] = dist;
			}
		}
		
		if( maxFrontWinding[i] > maxFront )
		{
			maxFront = maxFrontWinding[i];
		}
		if( maxBackWinding[i] < maxBack )
		{
			maxBack = maxBackWinding[i];
		}
	}
	
	if( maxFront < BRUSH_EPSILON )
	{
		if( back )
		{
			*back = Copy();
		}
		return PLANESIDE_BACK;
	}
	
	if( maxBack > -BRUSH_EPSILON )
	{
		if( front )
		{
			*front = Copy();
		}
		return PLANESIDE_FRONT;
	}
	
	mid = new idWinding( plane.Normal(), plane.Dist() );
	
	for( i = 0; i < sides.Num() && mid; i++ )
	{
		mid = mid->Clip( -sides[i]->plane, BRUSH_EPSILON, false );
	}
	
	if( mid )
	{
		if( mid->IsTiny() )
		{
			delete mid;
			mid = NULL;
		}
		else if( mid->IsHuge() )
		{
			// if the winding is huge then the brush is unbounded
			common->Warning( "brush %d on entity %d is unbounded"
							 "( %1.2f %1.2f %1.2f )-( %1.2f %1.2f %1.2f )-( %1.2f %1.2f %1.2f )", primitiveNum, entityNum,
							 bounds[0][0], bounds[0][1], bounds[0][2], bounds[1][0], bounds[1][1], bounds[1][2],
							 bounds[1][0] - bounds[0][0], bounds[1][1] - bounds[0][1], bounds[1][2] - bounds[0][2] );
			delete mid;
			mid = NULL;
		}
	}
	
	if( !mid )
	{
		if( maxFront > - maxBack )
		{
			if( front )
			{
				*front = Copy();

/*
============
idBrushBSPNode::Split
============
*/
bool idBrushBSPNode::Split( const idPlane &splitPlane, int splitPlaneNum ) {
	int s, i;
	idWinding *mid;
	idBrushBSPPortal *p, *midPortal, *newPortals[2];
	idBrushBSPNode *newNodes[2];

	mid = new idWinding( splitPlane.Normal(), splitPlane.Dist() );

	for ( p = portals; p && mid; p = p->next[s] ) {
		s = (p->nodes[1] == this);
		if ( s ) {
			mid = mid->Clip( -p->plane, 0.1f, false );
		}
		else {
			mid = mid->Clip( p->plane, 0.1f, false );
		}
	}

	if ( !mid ) {
		return false;
	}

	// allocate two new nodes
	for ( i = 0; i < 2; i++ ) {
		newNodes[i] = new idBrushBSPNode();
		newNodes[i]->flags = flags;
		newNodes[i]->contents = contents;
		newNodes[i]->parent = this;
	}

	// split all portals of the node
	for ( p = portals; p; p = portals ) {
		s = (p->nodes[1] == this);
		p->Split( splitPlane, &newPortals[0], &newPortals[1] );
		for ( i = 0; i < 2; i++ ) {
			if ( newPortals[i] ) {
				if ( s ) {
					newPortals[i]->AddToNodes( p->nodes[0], newNodes[i] );
				}
				else {
					newPortals[i]->AddToNodes( newNodes[i], p->nodes[1] );
				}
			}
		}
		p->RemoveFromNode( p->nodes[0] );
		p->RemoveFromNode( p->nodes[1] );
		delete p;
	}

	// add seperating portal
	midPortal = new idBrushBSPPortal();
	midPortal->plane = splitPlane;
	midPortal->planeNum = splitPlaneNum;
	midPortal->winding = mid;
	midPortal->AddToNodes( newNodes[0], newNodes[1] );

	// set new child nodes
	children[0] = newNodes[0];
	children[1] = newNodes[1];
	plane = splitPlane;

	return true;
}

/*
=================
idRenderModelDecal::CreateDecal
=================
*/
void idRenderModelDecal::CreateDecal( const idRenderModel *model, const decalProjectionParms_t &localParms ) {
	int maxVerts = 0;
	for ( int surfNum = 0; surfNum < model->NumSurfaces(); surfNum++ ) {
		const modelSurface_t *surf = model->Surface( surfNum );
		if ( surf->geometry != NULL && surf->shader != NULL ) {
			maxVerts = Max( maxVerts, surf->geometry->numVerts );
		}
	}

	idTempArray< byte > cullBits( ALIGN( maxVerts, 4 ) );

	// check all model surfaces
	for ( int surfNum = 0; surfNum < model->NumSurfaces(); surfNum++ ) {
		const modelSurface_t *surf = model->Surface( surfNum );

		// if no geometry or no shader
		if ( surf->geometry == NULL || surf->shader == NULL ) {
			continue;
		}

		// decals and overlays use the same rules
		if ( !localParms.force && !surf->shader->AllowOverlays() ) {
			continue;
		}

		srfTriangles_t *tri = surf->geometry;

		// if the triangle bounds do not overlap with the projection bounds
		if ( !localParms.projectionBounds.IntersectsBounds( tri->bounds ) ) {
			continue;
		}

		// decals don't work on animated models
		assert( tri->staticModelWithJoints == NULL );

		// catagorize all points by the planes
		R_DecalPointCullStatic( cullBits.Ptr(), localParms.boundingPlanes, tri->verts, tri->numVerts );

		// start streaming the indexes
		idODSStreamedArray< triIndex_t, 256, SBT_QUAD, 3 > indexesODS( tri->indexes, tri->numIndexes );

		// find triangles inside the projection volume
		for ( int i = 0; i < tri->numIndexes; ) {

			const int nextNumIndexes = indexesODS.FetchNextBatch() - 3;

			for ( ; i <= nextNumIndexes; i += 3 ) {
				const int i0 = indexesODS[i + 0];
				const int i1 = indexesODS[i + 1];
				const int i2 = indexesODS[i + 2];

				// skip triangles completely off one side
				if ( cullBits[i0] & cullBits[i1] & cullBits[i2] ) {
					continue;
				}

				const idDrawVert * verts[3] = {
					&tri->verts[i0],
					&tri->verts[i1],
					&tri->verts[i2]
				};

				// skip back facing triangles
				const idPlane plane( verts[0]->xyz, verts[1]->xyz, verts[2]->xyz );
				if ( plane.Normal() * localParms.boundingPlanes[NUM_DECAL_BOUNDING_PLANES - 2].Normal() < -0.1f ) {
					continue;
				}

				// create a winding with texture coordinates for the triangle
				idFixedWinding fw;
				fw.SetNumPoints( 3 );
				if ( localParms.parallel ) {
					for ( int j = 0; j < 3; j++ ) {
						fw[j] = verts[j]->xyz;
						fw[j].s = localParms.textureAxis[0].Distance( verts[j]->xyz );
						fw[j].t = localParms.textureAxis[1].Distance( verts[j]->xyz );
					}
				} else {
					for ( int j = 0; j < 3; j++ ) {
						const idVec3 dir = verts[j]->xyz - localParms.projectionOrigin;
						float scale;
						localParms.boundingPlanes[NUM_DECAL_BOUNDING_PLANES - 1].RayIntersection( verts[j]->xyz, dir, scale );
						const idVec3 intersection = verts[j]->xyz + scale * dir;

						fw[j] = verts[j]->xyz;
						fw[j].s = localParms.textureAxis[0].Distance( intersection );
						fw[j].t = localParms.textureAxis[1].Distance( intersection );
					}
				}

				const int orBits = cullBits[i0] | cullBits[i1] | cullBits[i2];

				// clip the exact surface triangle to the projection volume
				for ( int j = 0; j < NUM_DECAL_BOUNDING_PLANES; j++ ) {
					if ( ( orBits & ( 1 << j ) ) != 0 ) {
//.........这里部分代码省略.........

/*
================
idCollisionModelManagerLocal::PointFurthestFromPlane

  calculates the direction of motion at the initial position, where dir < 0 means the point moves towards the plane
  if the point moves away from the plane the tangent of half the rotation angle at which
  the point is furthest away from the plane is also calculated
================
*/
int idCollisionModelManagerLocal::PointFurthestFromPlane( const cm_traceWork_t *tw, const idVec3 &point, const idPlane &plane,
													const float angle, float &tanHalfAngle, float &dir ) {

	double v1, v2, a, b, c, d, sqrtd, q, frac1, frac2;
	idVec3 p, normal;

	/*

	v2 * cos(t) + v1 * sin(t) + v0 = 0;

	// rotation about the z-axis
	v0 = normal[2] * p[2] + dist
	v1 = normal[0] * p[1] - normal[1] * p[0]
	v2 = normal[0] * p[0] + normal[1] * p[1]

	derivative:
	v1 * cos(t) - v2 * sin(t) = 0;

	r = tan(t / 2);
	sin(t) = 2*r/(1+r*r);
	cos(t) = (1-r*r)/(1+r*r);

	-v2 * 2 * r / (1 + r*r) + v1 * (1 - r*r)/(1+r*r);
	-v2 * 2 * r + v1 * (1 - r*r) / (1 + r*r) = 0;
	-v2 * 2 * r + v1 * (1 - r*r) = 0;
	(-v1) * r * r + (-2 * v2) * r + (v1) = 0;

	*/

	tanHalfAngle = 0.0f;

	// transform rotation axis to z-axis
	p = (point - tw->origin) * tw->matrix;
	normal = plane.Normal() * tw->matrix;

	v1 = normal[0] * p[1] - normal[1] * p[0];
	v2 = normal[0] * p[0] + normal[1] * p[1];

	// the point will always start at the front of the plane, therefore v0 + v2 > 0 is always true
	if ( angle < 0.0f ) {
		dir = -v1;
	}
	else {
		dir = v1;
	}
	// negative direction means the point moves towards the plane at the initial position
	if ( dir <= 0.0f ) {
		return true;
	}

	a = -v1;
	b = -v2;
	c = v1;
	if ( a == 0.0f ) {
		if ( b == 0.0f ) {
			return false;
		}
		frac1 = -c / ( 2.0f * b );
		frac2 = 1e10;	// = tan( idMath::HALF_PI )
	}
	else {
		d = b * b - c * a;
		if ( d <= 0.0f ) {
			return false;
		}
		sqrtd = sqrt( d );
		if ( b > 0.0f ) {
			q = - b + sqrtd;
		}
		else {
			q = - b - sqrtd;
		}
		frac1 = q / a;
		frac2 = c / q;
	}

	if ( angle < 0.0f ) {
		frac1 = -frac1;
		frac2 = -frac2;
	}

	if ( frac1 < 0.0f && frac2 < 0.0f ) {
		return false;
	}

	if ( frac1 > frac2 ) {
		tanHalfAngle = frac1;
	}
	else {
		tanHalfAngle = frac2;
	}
//.........这里部分代码省略.........

/*
================
idCollisionModelManagerLocal::RotatePointThroughPlane

  calculates the tangent of half the rotation angle at which the point collides with the plane
================
*/
int idCollisionModelManagerLocal::RotatePointThroughPlane( const cm_traceWork_t *tw, const idVec3 &point, const idPlane &plane,
													const float angle, const float minTan, float &tanHalfAngle ) {
	double v0, v1, v2, a, b, c, d, sqrtd, q, frac1, frac2;
	idVec3 p, normal;

	/*

	p[0] = point[0] * cos(t) + point[1] * sin(t)
	p[1] = point[0] * -sin(t) + point[1] * cos(t)
	p[2] = point[2];

	normal[0] * (p[0] * cos(t) + p[1] * sin(t)) +
		normal[1] * (p[0] * -sin(t) + p[1] * cos(t)) +
			normal[2] * p[2] + dist = 0

	normal[0] * p[0] * cos(t) + normal[0] * p[1] * sin(t) +
		-normal[1] * p[0] * sin(t) + normal[1] * p[1] * cos(t) +
			normal[2] * p[2] + dist = 0

	v2 * cos(t) + v1 * sin(t) + v0

	// rotation about the z-axis
	v0 = normal[2] * p[2] + dist
	v1 = normal[0] * p[1] - normal[1] * p[0]
	v2 = normal[0] * p[0] + normal[1] * p[1]

	r = tan(t / 2);
	sin(t) = 2*r/(1+r*r);
	cos(t) = (1-r*r)/(1+r*r);

	v1 * 2 * r / (1 + r*r) + v2 * (1 - r*r) / (1 + r*r) + v0 = 0
	(v1 * 2 * r + v2 * (1 - r*r)) / (1 + r*r) = -v0
	(v1 * 2 * r + v2 - v2 * r*r) / (1 + r*r) = -v0
	v1 * 2 * r + v2 - v2 * r*r = -v0 * (1 + r*r)
	v1 * 2 * r + v2 - v2 * r*r = -v0 + -v0 * r*r
	(v0 - v2) * r * r + (2 * v1) * r + (v0 + v2) = 0;

	*/

	tanHalfAngle = tw->maxTan;

	// transform rotation axis to z-axis
	p = (point - tw->origin) * tw->matrix;
	d = plane[3] + plane.Normal() * tw->origin;
	normal = plane.Normal() * tw->matrix;

	v0 = normal[2] * p[2] + d;
	v1 = normal[0] * p[1] - normal[1] * p[0];
	v2 = normal[0] * p[0] + normal[1] * p[1];

	a = v0 - v2;
	b = v1;
	c = v0 + v2;
	if ( a == 0.0f ) {
		if ( b == 0.0f ) {
			return false;
		}
		frac1 = -c / ( 2.0f * b );
		frac2 = 1e10;	// = tan( idMath::HALF_PI )
	}
	else {
		d = b * b - c * a;
		if ( d <= 0.0f ) {
			return false;
		}
		sqrtd = sqrt( d );
		if ( b > 0.0f ) {
			q = - b + sqrtd;
		}
		else {
			q = - b - sqrtd;
		}
		frac1 = q / a;
		frac2 = c / q;
	}

	if ( angle < 0.0f ) {
		frac1 = -frac1;
		frac2 = -frac2;
	}

	// get smallest tangent for which a collision occurs
	if ( frac1 >= minTan && frac1 < tanHalfAngle ) {
		tanHalfAngle = frac1;
	}
	if ( frac2 >= minTan && frac2 < tanHalfAngle ) {
		tanHalfAngle = frac2;
	}

	if ( angle < 0.0f ) {
		tanHalfAngle = -tanHalfAngle;
	}

//.........这里部分代码省略.........