19 const auto ab = ( b - a ).lengthSq();
20 const auto ca = ( a - c ).lengthSq();
21 const auto bc = ( c - b ).lengthSq();
28 const auto f = cross( b - a, c - a ).lengthSq();
30 return std::numeric_limits<T>::infinity();
31 return ab * ca * bc / f;
46 const auto xabSq = cross( a, b ).lengthSq();
56 const auto ab = dot( a, b );
57 return ( bb * ( aa - ab ) * a + aa * ( bb - ab ) * b ) / ( 2 * xabSq );
74 const auto rr =
sqr( radius );
79 const auto x = std::sqrt( rr - circRadSq );
80 const auto xn = x *
normal( a, b, c );
82 centerPos = circCenter + xn;
83 centerNeg = circCenter - xn;
93 const auto ab = ( b - a ).
length();
94 const auto ca = ( a - c ).
length();
95 const auto bc = ( c - b ).
length();
96 if ( ab <= 0 || ca <= 0 || bc <= 0 )
98 const auto f = cross( b - a, c - a ).length();
99 return f * std::min( { ab, ca, bc } ) / ( ab * ca * bc );
113 const auto bc = ( c - b ).
length();
114 const auto ca = ( a - c ).
length();
115 const auto ab = ( b - a ).
length();
116 auto halfPerimeter = ( bc + ca + ab ) / 2;
117 auto den = 8 * ( halfPerimeter - bc ) * ( halfPerimeter - ca ) * ( halfPerimeter - ab );
119 return std::numeric_limits<T>::max();
121 return bc * ca * ab / den;
128 return cross( t[1] - t[0], t[2] - t[0] );
135 return cross( q, r );
142 return cross( q - p, r - p );
156 return normal( q - p, r - p );
168[[nodiscard]]
inline T
dblArea(
const Triangle3<T> & t )
191 return std::abs( cross( q - p, r - p ) );
205 const auto c = ( t[0] + t[1] + t[2] ) / T(3);
208 for (
int i = 0; i < 3; ++i )
210 const auto sq = ( t[i] - c ).lengthSq();
211 if ( longestSq >= sq )
216 const auto d = ( t[longest] - c ).normalized();
220 for (
int i = 0; i < 3; ++i )
221 res[i] = c + d * dot( d, t[i] - c );
230 const auto c = ( t[0] + t[1] + t[2] ) / T(3);
232 for (
int i = 0; i < 3; ++i )
233 res[i] = t[i] - n * dot( n, t[i] - c );
249 return dot( edgeDir, cross( leftNorm, rightNorm ) );
260 return dot( leftNorm, rightNorm );
274 return std::atan2( sin, cos );
290 const auto aa =
sqr( a );
291 const auto y = ( aa -
sqr( b ) +
sqr( c ) ) / ( 2 * c );
292 const auto yy =
sqr( y );
295 const auto x = std::sqrt( aa - yy );
313 auto y = ( p->x * p1->y - p1->x * p->y ) / ( p->x - p1->x );
314 if ( y < 0 || y > c )
316 return ( *p - *p1 ).length();
325 const T den = ( a + b + c ) * ( b + c - a );
327 return std::numeric_limits<T>::infinity();
328 const T num = ( a + c - b ) * ( a + b - c );
337[[nodiscard]]
inline T
cotan(
const Triangle3<T> & t, T absMaxVal = std::numeric_limits<T>::max() )
339 auto a = t[0] - t[2];
340 auto b = t[1] - t[2];
341 auto nom = dot( a, b );
342 auto den = cross( a, b ).length();
343 if ( fabs( nom ) >= absMaxVal * den )
344 return absMaxVal *
sgn( nom );
352[[nodiscard]]
inline T
cotan( T a, T b, T c )
354 const T den = ( a + b + c ) * ( b + c - a );
356 return -std::numeric_limits<T>::infinity();
357 const T num = ( a + c - b ) * ( a + b - c );
359 return std::numeric_limits<T>::infinity();
360 const auto tanSq = num / den;
361 return ( 1 - tanSq ) / ( 2 * std::sqrt( tanSq ) );
369 const auto bb = dot( b, b );
370 const auto bc = dot( b, c );
371 const auto cc = dot( c, c );
372 const auto det = bb * cc - bc * bc;
375 const auto kb = ( 1 / det ) * ( cc * vb - bc * vc );
376 const auto kc = ( 1 / det ) * (-bc * vb + bb * vc );
377 return kb * b + kc * c;
393 const auto gradSq = grad.
lengthSq();
396 const auto d = c - b;
398 const auto gort = d - ( dot( d, grad ) / gradSq ) * grad;
399 const auto god = dot( gort, d );
402 const auto gob = -dot( gort, b );
403 if ( gob <= 0 || gob >= god )
405 const auto a = gob / god;
406 assert( a < std::numeric_limits<T>::max() );
407 const auto ip = a * c + ( 1 - a ) * b;
408 if ( dot( grad, ip ) >= 0 )
423 if ( !grad.has_value() )
425 auto gradSq = grad->lengthSq();
428 return sqrt( 1 - gradSq ) *
normal( b, c ) - *grad;
441 return Plane3<T>( *n, dot( *n, a ) + ra );
length
Definition MRObjectDimensionsEnum.h:14
T minTriangleAngleSin(const Vector3< T > &a, const Vector3< T > &b, const Vector3< T > &c)
Definition MRTriMath.h:91
float area(const MeshTopology &topology, const VertCoords &points, FaceId f)
returns the area of given face
Definition MRMeshMath.h:166
constexpr T sqr(T x) noexcept
squared value
Definition MRMesh/MRMeshFwd.h:666
MRMESH_API float circumcircleDiameter(const MeshTopology &topology, const VertCoords &points, FaceId f)
returns circumcircle diameter of given mesh triangle
MRMESH_API float dihedralAngle(const MeshTopology &topology, const VertCoords &points, UndirectedEdgeId e)
Vector3< T > circumcircleCenter(const Vector3< T > &a, const Vector3< T > &b)
Computes the center of the the triangle's 0AB circumcircle.
Definition MRTriMath.h:44
MRMESH_API float dihedralAngleCos(const MeshTopology &topology, const VertCoords &points, UndirectedEdgeId e)
std::optional< T > findTriExitPos(const Vector3< T > &b, const Vector3< T > &c, const Vector3< T > &grad)
Definition MRTriMath.h:391
std::optional< T > quadrangleOtherDiagonal(T a, T b, T c, T a1, T b1)
Definition MRTriMath.h:303
Triangle3< T > makeDegenerate(const Triangle3< T > &t)
make degenerate triangle (all 3 points on a line) that maximally resembles the input one and has the ...
Definition MRTriMath.h:203
T tanSqOfHalfAngle(T a, T b, T c)
Definition MRTriMath.h:323
Triangle3< T > triangleWithNormal(const Triangle3< T > &t, const Vector3< T > &n)
Definition MRTriMath.h:228
Vector3f dirDblArea(const MeshTopology &topology, const VertCoords &points, FaceId f)
computes directed double area for a triangular face from its vertices
Definition MRMeshMath.h:151
MRMESH_API float triangleAspectRatio(const MeshTopology &topology, const VertCoords &points, FaceId f)
returns aspect ratio of given mesh triangle equal to the ratio of the circum-radius to twice its in-r...
constexpr int sgn(T x) noexcept
sign of given value in { -1, 0, 1 }
Definition MRMesh/MRMeshFwd.h:670
std::optional< Vector3< T > > gradientInTri(const Vector3< T > &b, const Vector3< T > &c, T vb, T vc)
Definition MRTriMath.h:367
std::optional< Plane3< T > > tangentPlaneToSpheres(const Vector3< T > &a, const Vector3< T > &b, const Vector3< T > &c, T ra, T rb, T rc)
Definition MRTriMath.h:438
MRMESH_API float circumcircleDiameterSq(const MeshTopology &topology, const VertCoords &points, FaceId f)
returns squared circumcircle diameter of given mesh triangle
bool circumballCenters(const Vector3< T > &a, const Vector3< T > &b, const Vector3< T > &c, T radius, Vector3< T > ¢erPos, Vector3< T > ¢erNeg)
Definition MRTriMath.h:70
std::optional< Vector3< T > > tangentPlaneNormalToSpheres(const Vector3< T > &b, const Vector3< T > &c, T rb, T rc)
Definition MRTriMath.h:420
float dblArea(const MeshTopology &topology, const VertCoords &points, FaceId f)
returns twice the area of given face
Definition MRMeshMath.h:160
T minTriangleAngle(const Vector3< T > &a, const Vector3< T > &b, const Vector3< T > &c)
Definition MRTriMath.h:103
std::optional< Vector2< T > > posFromTriEdgeLengths(T a, T b, T c)
Definition MRTriMath.h:281
float cotan(const MeshTopology &topology, const VertCoords &points, UndirectedEdgeId ue)
Definition MRMeshMath.h:306
T dblAreaSq(const Vector3< T > &p, const Vector3< T > &q, const Vector3< T > &r)
computes the square of double area of given triangle
Definition MRTriMath.h:161
MRMESH_API float dihedralAngleSin(const MeshTopology &topology, const VertCoords &points, UndirectedEdgeId e)
Definition MRVector2.h:25
Definition MRMesh/MRVector3.h:26
Vector3 normalized() const
Definition MRMesh/MRVector3.h:62
T lengthSq() const
Definition MRMesh/MRVector3.h:53