25 if ( p1 && p2 && p3 && result )
28 const double area =
triArea( p1, p2, p3 );
33 const double area1 =
triArea( &p, p2, p3 );
34 const double area2 =
triArea( p1, &p, p3 );
35 const double area3 =
triArea( p1, p2, &p );
36 const double u = area1 / area;
37 const double v = area2 / area;
38 const double w = area3 / area;
56 if ( p1 && p2 && p3 && result )
58 const double area =
triArea( p1, p2, p3 );
62 QgsDebugError( QStringLiteral(
"warning, p1, p2 and p3 are in a line" ) );
66 const double denominator = ( ( p2->
y() - p3->
y() ) * ( p1->
x() - p3->
x() ) - ( p3->
y() - p1->
y() ) * ( p3->
x() - p2->
x() ) );
67 if ( denominator != 0 )
69 px = ( 2 * u * area * ( p1->
x() - p3->
x() ) - 2 * v * area * ( p3->
x() - p2->
x() ) - p2->
x() * p3->
y() * ( p1->
x() - p3->
x() ) + p3->
x() * p1->
y() * ( p3->
x() - p2->
x() ) + p3->
x() * p2->
y() * ( p1->
x() - p3->
x() ) - p1->
x() * p3->
y() * ( p3->
x() - p2->
x() ) ) / denominator;
70 if ( ( p3->
x() - p2->
x() ) != 0 )
72 py = ( 2 * u * area - px * ( p2->
y() - p3->
y() ) - p2->
x() * p3->
y() + p3->
x() * p2->
y() ) / ( p3->
x() - p2->
x() );
76 py = ( 2 * v * area - px * ( p3->
y() - p1->
y() ) - p3->
x() * p1->
y() + p1->
x() * p3->
y() ) / ( p1->
x() - p3->
x() );
81 py = ( 2 * u * area * ( p3->
y() - p1->
y() ) - 2 * v * area * ( p2->
y() - p3->
y() ) - p2->
x() * p3->
y() * ( p3->
y() - p1->
y() ) + p3->
x() * p1->
y() * ( p2->
y() - p3->
y() ) + p3->
x() * p2->
y() * ( p3->
y() - p1->
y() ) - p1->
x() * p3->
y() * ( p2->
y() - p3->
y() ) ) / ( ( p3->
x() - p2->
x() ) * ( p3->
y() - p1->
y() ) - ( p1->
x() - p3->
x() ) * ( p2->
y() - p3->
y() ) );
82 if ( ( p2->
y() - p3->
y() ) != 0 )
84 px = ( 2 * u * area - py * ( p3->
x() - p2->
x() ) - p2->
x() * p3->
y() + p3->
x() * p2->
y() ) / ( p2->
y() - p3->
y() );
88 px = ( 2 * v * area - py * ( p1->
x() - p3->
x() ) - p3->
x() * p1->
y() + p1->
x() * p3->
y() ) / ( p3->
y() - p1->
y() );
109 return lower( n, i ) * std::pow( t, i ) * std::pow( ( 1 - t ), ( n - i ) );
119 if ( p1 && p2 && p3 && result )
121 const double distp1p2 = p1->
distance( *p2 );
122 const double distp2p3 = p2->
distance( *p3 );
123 if ( distp1p2 > distp2p3 )
130 const double denominator = -p3->
x() * p2->
y() + p3->
x() * p1->
y() + p1->
x() * p2->
y() + p2->
x() * p3->
y() - p2->
x() * p1->
y() - p1->
x() * p3->
y();
132 if ( denominator == 0 )
134 QgsDebugError( QStringLiteral(
"error: the three points are in a line" ) );
139 result->
setX( 0.5 * ( p1->
x()*p1->
x()*p2->
y() - p1->
x()*p1->
x()*p3->
y() - p3->
x()*p3->
x()*p2->
y() - p1->
y()*p2->
x()*p2->
x() - p1->
y()*p1->
y()*p3->
y() - p3->
y()*p3->
y()*p2->
y() + p1->
y()*p1->
y()*p2->
y() + p3->
y()*p2->
x()*p2->
x() - p1->
y()*p2->
y()*p2->
y() + p1->
y()*p3->
y()*p3->
y() + p1->
y()*p3->
x()*p3->
x() + p3->
y()*p2->
y()*p2->
y() ) / denominator );
140 result->
setY( -0.5 * ( p3->
x()*p2->
x()*p2->
x() + p2->
x()*p1->
y()*p1->
y() + p3->
x()*p2->
y()*p2->
y() - p3->
x()*p1->
x()*p1->
x() + p1->
x()*p3->
y()*p3->
y() - p3->
x()*p1->
y()*p1->
y() - p1->
x()*p2->
x()*p2->
x() - p2->
x()*p3->
y()*p3->
y() - p1->
x()*p2->
y()*p2->
y() - p2->
x()*p3->
x()*p3->
x() + p1->
x()*p3->
x()*p3->
x() + p2->
x()*p1->
x()*p1->
x() ) / denominator );
154 if ( thepoint && p1 && p2 )
157 Vector3D line( p2->
x() - p1->
x(), p2->
y() - p1->
y(), 0 );
159 const double a = normal.
getX();
160 const double b = normal.
getY();
161 const double c = -( normal.
getX() * p2->
x() + normal.
getY() * p2->
y() );
162 const double distance = std::fabs( ( a * thepoint->
x() + b * thepoint->
y() +
c ) / ( std::sqrt( a * a + b * b ) ) );
174 return std::tgamma( n + 1 );
179 const double tolerance = 0.0001;
181 if ( testp && p1 && p2 && p3 )
189 double px = testp->
x();
190 double py = testp->
y();
192 const double xmin = std::min( std::min( ax, px ), std::min( bx, cx ) );
193 const double ymin = std::min( std::min( ay, py ), std::min( by, cy ) );
203 double aValue = ( ax * ax + ay * ay ) *
triArea( p2, p3, testp );
204 aValue = aValue - ( ( bx * bx + by * by ) *
triArea( p1, p3, testp ) );
205 aValue = aValue + ( ( cx * cx + cy * cy ) *
triArea( p1, p2, testp ) );
206 aValue = aValue - ( ( px * px + py * py ) *
triArea( p1, p2, p3 ) );
208 return aValue > tolerance;
219 return angle( p1, point, p2, point ) > 90;
227 const double f1 = thepoint.
x() - p1->
x();
228 const double f2 = p2->
y() - p1->
y();
229 const double f3 = thepoint.
y() - p1->
y();
230 const double f4 = p2->
x() - p1->
x();
231 return f1 * f2 - f3 * f4;
243 if ( p1 && p2 && p3 && p4 )
246 const Vector3D p1p2( p2->
x() - p1->
x(), p2->
y() - p1->
y(), 0 );
247 const Vector3D p3p4( p4->
x() - p3->
x(), p4->
y() - p3->
y(), 0 );
251 t1 = ( p3->
x() - p1->
x() + t2 * p3p4.
getX() ) / p1p2.
getX();
256 t2 = ( p1->
x() + t1 * p1p2.
getX() - p3->
x() ) / p3p4.
getX();
263 if ( t1 > 0 && t1 < 1 && t2 > 0 && t2 < 1 )
265 if ( ( *p1 ) == ( *p3 ) || ( *p1 ) == ( *p4 ) || ( *p2 ) == ( *p3 ) || ( *p2 ) == ( *p4 ) )
286 if ( p1 && p2 && p3 && p4 )
289 const Vector3D p1p2( p2->
x() - p1->
x(), p2->
y() - p1->
y(), 0 );
290 const Vector3D p3p4( p4->
x() - p3->
x(), p4->
y() - p3->
y(), 0 );
294 t1 = ( p3->
x() - p1->
x() + t2 * p3p4.
getX() ) / p1p2.
getX();
299 t2 = ( p1->
x() + t1 * p1p2.
getX() - p3->
x() ) / p3p4.
getX();
303 intersection_point->
setX( 0 );
304 intersection_point->
setY( 0 );
305 intersection_point->
setZ( 0 );
309 if ( t1 > 0 && t1 < 1 && t2 > 0 && t2 < 1 )
311 if ( ( *p1 ) == ( *p3 ) || ( *p1 ) == ( *p4 ) || ( *p2 ) == ( *p3 ) || ( *p2 ) == ( *p4 ) )
313 intersection_point->
setX( 0 );
314 intersection_point->
setY( 0 );
315 intersection_point->
setZ( 0 );
319 intersection_point->
setX( p1->
x() * ( 1 - t1 ) + p2->
x()*t1 );
320 intersection_point->
setY( p1->
y() * ( 1 - t1 ) + p2->
y()*t1 );
321 intersection_point->
setZ( 0 );
339 if ( i >= 0 && i <= n )
351 if ( pa && pb && pc )
353 const double deter = ( pa->
x() * pb->
y() + pb->
x() * pc->
y() + pc->
x() * pa->
y() - pa->
x() * pc->
y() - pb->
x() * pa->
y() - pc->
x() * pb->
y() );
365 if ( n != 3 || i > n )
367 QgsDebugError( QStringLiteral(
"error, can't calculate hermite polynom" ) );
370 if ( n == 3 && i == 0 )
375 if ( n == 3 && i == 1 )
380 if ( n == 3 && i == 2 )
385 if ( n == 3 && i == 3 )
398 if ( n != 3 || i > n )
400 QgsDebugError( QStringLiteral(
"error, can't calculate hermite polynom" ) );
403 if ( n == 3 && i == 0 )
410 if ( n == 3 && i == 1 )
416 if ( n == 3 && i == 2 )
422 if ( n == 3 && i == 3 )
437 if ( v1 && v2 && result )
454 if ( v1->
getY() == 0 )
458 if ( v1->
getX() < 0 )
460 result->
setY( -length );
465 result->
setY( length );
471 const double a = 1 + ( v1->
getX() * v1->
getX() ) / ( v1->
getY() * v1->
getY() );
473 const double c = -( length * length );
474 const double d = b * b - 4 * a *
c;
482 result->
setX( ( -b + std::sqrt( d ) ) / ( 2 * a ) );
489 if ( !(
leftOf( point1, &point2, &point3 ) < 0 ) )
511 if ( v1->
getY() == 0 )
515 if ( v1->
getX() < 0 )
517 result->
setY( length );
522 result->
setY( -length );
528 const double a = 1 + ( v1->
getX() * v1->
getX() ) / ( v1->
getY() * v1->
getY() );
530 const double c = -( length * length );
531 const double d = b * b - 4 * a *
c;
539 result->
setX( ( -b + std::sqrt( d ) ) / ( 2 * a ) );
546 if ( (
leftOf( point1, &point2, &point3 ) < 0 ) )
564 if ( p1 && p2 && p3 && vec )
566 const double ax = p2->
x() - p1->
x();
567 const double ay = p2->
y() - p1->
y();
568 const double az = p2->
z() - p1->
z();
569 const double bx = p3->
x() - p1->
x();
570 const double by = p3->
y() - p1->
y();
571 const double bz = p3->
z() - p1->
z();
573 vec->
setX( ay * bz - az * by );
574 vec->
setY( az * bx - ax * bz );
575 vec->
setZ( ax * by - ay * bx );
582 if ( first && vec1 && second && vec2 )
592 return ( ( first->
x() * vec1->
getY() - first->
y() * vec1->
getX() - second->
x() * vec1->
getY() + second->
y() * vec1->
getX() ) / ( vec2->
getX() * vec1->
getY() - vec2->
getY() * vec1->
getX() ) );
597 QgsDebugError( QStringLiteral(
"warning: vectors are parallel" ) );
630 if ( tangent && target && result )
632 const double xt = tangent->
getX();
633 const double yt = tangent->
getY();
634 const double zt = tangent->
getZ();
636 const double xw = target->
getX();
637 const double yw = target->
getY();
638 const double zw = target->
getZ();
640 double xg1, yg1, zg1;
641 double xg2, yg2, zg2;
644 const double xgalpha1 = 1 / ( 2 * xt * xt * yw * yw * zt * zt - 2 * zt * zt * zt * xt * zw * xw + yt * yt * yt * yt * zw * zw + yt * yt * zw * zw * zt * zt + xt * xt * yt * yt * xw * xw + xt * xt * yw * yw * yt * yt - 2 * xt * xt * xt * zt * zw * xw + yt * yt * yt * yt * xw * xw + yt * yt * yw * yw * zt * zt + 2 * xt * xt * yt * yt * zw * zw - 2 * yt * yt * yt * yw * zt * zw + zt * zt * xt * xt * zw * zw + zt * zt * zt * zt * xw * xw + xt * xt * zt * zt * xw * xw + 2 * zt * zt * xw * xw * yt * yt - 2 * xt * xt * yw * zt * yt * zw - 2 * xt * yt * yt * yt * xw * yw - 2 * xt * xt * xt * yw * yt * xw - 2 * xt * zt * zt * xw * yt * yw - 2 * xt * zt * xw * yt * yt * zw - 2 * yw * zt * zt * zt * yt * zw + xt * xt * xt * xt * yw * yw + yw * yw * zt * zt * zt * zt + xt * xt * xt * xt * zw * zw );
647 QgsDebugError( QStringLiteral(
"warning, only complex solution of xg" ) );
650 xg1 = std::sqrt( xgalpha1 ) * ( -yt * yw * xt + yt * yt * xw + xw * zt * zt - zt * xt * zw );
651 xg2 = -sqrt( xgalpha1 ) * ( -yt * yw * xt + yt * yt * xw + xw * zt * zt - zt * xt * zw );
654 const double ygalpha1 = 1 / ( 2 * xt * xt * yw * yw * zt * zt - 2 * zt * zt * zt * xt * zw * xw + yt * yt * yt * yt * zw * zw + yt * yt * zw * zw * zt * zt + xt * xt * yt * yt * xw * xw + xt * xt * yw * yw * yt * yt - 2 * xt * xt * xt * zt * zw * xw + yt * yt * yt * yt * xw * xw + yt * yt * yw * yw * zt * zt + 2 * xt * xt * yt * yt * zw * zw - 2 * yt * yt * yt * yw * zt * zw + zt * zt * xt * xt * zw * zw + zt * zt * zt * zt * xw * xw + xt * xt * zt * zt * xw * xw + 2 * zt * zt * xw * xw * yt * yt - 2 * xt * xt * yw * zt * yt * zw - 2 * xt * yt * yt * yt * xw * yw - 2 * xt * xt * xt * yw * yt * xw - 2 * xt * zt * zt * xw * yt * yw - 2 * xt * zt * xw * yt * yt * zw - 2 * yw * zt * zt * zt * yt * zw + xt * xt * xt * xt * yw * yw + yw * yw * zt * zt * zt * zt + xt * xt * xt * xt * zw * zw );
657 QgsDebugError( QStringLiteral(
"warning, only complex solution of yg" ) );
660 yg1 = -sqrt( ygalpha1 ) * ( -yw * xt * xt - zt * zt * yw + zt * yt * zw + yt * xw * xt );
661 yg2 = std::sqrt( ygalpha1 ) * ( -yw * xt * xt - zt * zt * yw + zt * yt * zw + yt * xw * xt );
664 const double zgalpha1 = 1 / ( 2 * xt * xt * yw * yw * zt * zt - 2 * zt * zt * zt * xt * zw * xw + yt * yt * yt * yt * zw * zw + yt * yt * zw * zw * zt * zt + xt * xt * yt * yt * xw * xw + xt * xt * yw * yw * yt * yt - 2 * xt * xt * xt * zt * zw * xw + yt * yt * yt * yt * xw * xw + yt * yt * yw * yw * zt * zt + 2 * xt * xt * yt * yt * zw * zw - 2 * yt * yt * yt * yw * zt * zw + zt * zt * xt * xt * zw * zw + zt * zt * zt * zt * xw * xw + xt * xt * zt * zt * xw * xw + 2 * zt * zt * xw * xw * yt * yt - 2 * xt * xt * yw * zt * yt * zw - 2 * xt * yt * yt * yt * xw * yw - 2 * xt * xt * xt * yw * yt * xw - 2 * xt * zt * zt * xw * yt * yw - 2 * xt * zt * xw * yt * yt * zw - 2 * yw * zt * zt * zt * yt * zw + xt * xt * xt * xt * yw * yw + yw * yw * zt * zt * zt * zt + xt * xt * xt * xt * zw * zw );
667 QgsDebugError( QStringLiteral(
"warning, only complex solution of zg" ) );
670 zg1 = -sqrt( zgalpha1 ) * ( yt * yw * zt - yt * yt * zw + xw * zt * xt - xt * xt * zw );
671 zg2 = std::sqrt( zgalpha1 ) * ( yt * yw * zt - yt * yt * zw + xw * zt * xt - xt * xt * zw );
676 if ( distance1 <= distance2 )
701 if ( test && pt1 && pt2 && pt3 )
703 const double a = ( pt1->
z() * ( pt2->
y() - pt3->
y() ) + pt2->
z() * ( pt3->
y() - pt1->
y() ) + pt3->
z() * ( pt1->
y() - pt2->
y() ) ) / ( ( pt1->
x() - pt2->
x() ) * ( pt2->
y() - pt3->
y() ) - ( pt2->
x() - pt3->
x() ) * ( pt1->
y() - pt2->
y() ) );
704 const double b = ( pt1->
z() * ( pt2->
x() - pt3->
x() ) + pt2->
z() * ( pt3->
x() - pt1->
x() ) + pt3->
z() * ( pt1->
x() - pt2->
x() ) ) / ( ( pt1->
y() - pt2->
y() ) * ( pt2->
x() - pt3->
x() ) - ( pt2->
y() - pt3->
y() ) * ( pt1->
x() - pt2->
x() ) );
705 const double c = pt1->
z() - a * pt1->
x() - b * pt1->
y();
706 const double zpredicted = test->
x() * a + test->
y() * b +
c;
707 return ( test->
z() - zpredicted );
718 if ( p1 && p2 && p3 && p4 )
720 const Vector3D v1( p2->
x() - p1->
x(), p2->
y() - p1->
y(), 0 );
721 const Vector3D v2( p4->
x() - p3->
x(), p4->
y() - p3->
y(), 0 );
static double distance2D(double x1, double y1, double x2, double y2)
Returns the 2D distance between (x1, y1) and (x2, y2).
Point geometry type, with support for z-dimension and m-values.
void setY(double y)
Sets the point's y-coordinate.
void setX(double x)
Sets the point's x-coordinate.
double distance(double x, double y) const
Returns the Cartesian 2D distance between this point and a specified x, y coordinate.
void setZ(double z)
Sets the point's z-coordinate.
Class Vector3D represents a 3D-Vector, capable to store x-,y- and z-coordinates in double values.
void setX(double x)
Sets the x-component of the vector.
double getY() const
Returns the y-component of the vector.
double getX() const
Returns the x-component of the vector.
void setY(double y)
Sets the y-component of the vector.
double getZ() const
Returns the z-component of the vector.
double getLength() const
Returns the length of the vector.
void setZ(double z)
Sets the z-component of the vector.
bool ANALYSIS_EXPORT normalLeft(Vector3D *v1, Vector3D *result, double length)
Assigns the vector 'result', which is normal to the vector 'v1', on the left side of v1 and has lengt...
bool ANALYSIS_EXPORT inDiametral(QgsPoint *p1, QgsPoint *p2, QgsPoint *point)
Tests, whether 'point' is inside the diametral circle through 'p1' and 'p2'.
bool ANALYSIS_EXPORT derVec(const Vector3D *v1, const Vector3D *v2, Vector3D *result, double x, double y)
Calculates the z-component of a vector with coordinates 'x' and 'y'which is in the same tangent plane...
double ANALYSIS_EXPORT calcBernsteinPoly(int n, int i, double t)
Calculates the value of a Bernstein polynomial.
int ANALYSIS_EXPORT faculty(int n)
Faculty function.
bool ANALYSIS_EXPORT BarycentricToXY(double u, double v, double w, QgsPoint *p1, QgsPoint *p2, QgsPoint *p3, QgsPoint *result)
double ANALYSIS_EXPORT angle(QgsPoint *p1, QgsPoint *p2, QgsPoint *p3, QgsPoint *p4)
Calculates the angle between two segments (in 2 dimension, z-values are ignored)
double ANALYSIS_EXPORT triArea(QgsPoint *pa, QgsPoint *pb, QgsPoint *pc)
Returns the area of a triangle. If the points are ordered counterclockwise, the value will be positiv...
bool ANALYSIS_EXPORT pointInsideTriangle(double x, double y, QgsPoint *p1, QgsPoint *p2, QgsPoint *p3)
Returns true, if the point with coordinates x and y is inside (or at the edge) of the triangle p1,...
bool ANALYSIS_EXPORT normalRight(Vector3D *v1, Vector3D *result, double length)
Assigns the vector 'result', which is normal to the vector 'v1', on the right side of v1 and has leng...
double ANALYSIS_EXPORT crossVec(QgsPoint *first, Vector3D *vec1, QgsPoint *second, Vector3D *vec2)
Calculates the intersection of the two vectors vec1 and vec2, which start at first(vec1) and second(v...
bool ANALYSIS_EXPORT lineIntersection(QgsPoint *p1, QgsPoint *p2, QgsPoint *p3, QgsPoint *p4)
Returns true, if line1 (p1 to p2) and line2 (p3 to p4) intersect. If the lines have an endpoint in co...
int ANALYSIS_EXPORT lower(int n, int i)
Lower function.
double ANALYSIS_EXPORT planeTest(QgsPoint *test, QgsPoint *pt1, QgsPoint *pt2, QgsPoint *pt3)
Tests, if 'test' is in the same plane as 'p1', 'p2' and 'p3' and returns the z-difference from the pl...
bool ANALYSIS_EXPORT circumcenter(QgsPoint *p1, QgsPoint *p2, QgsPoint *p3, QgsPoint *result)
Calculates the center of the circle passing through p1, p2 and p3. Returns true in case of success an...
double ANALYSIS_EXPORT cFDerBernsteinPoly(int n, int i, double t)
Calculates the first derivative of a Bernstein polynomial with respect to the parameter t.
double ANALYSIS_EXPORT cFDerCubicHermitePoly(int n, int i, double t)
Calculates the first derivative of a cubic Hermite polynomial with respect to the parameter t.
double ANALYSIS_EXPORT leftOf(const QgsPoint &thepoint, const QgsPoint *p1, const QgsPoint *p2)
Returns whether 'thepoint' is left or right of the line from 'p1' to 'p2'. Negative values mean left ...
double ANALYSIS_EXPORT distPointFromLine(QgsPoint *thepoint, QgsPoint *p1, QgsPoint *p2)
Calculates the (2 dimensional) distance from 'thepoint' to the line defined by p1 and p2.
bool ANALYSIS_EXPORT calcBarycentricCoordinates(double x, double y, QgsPoint *p1, QgsPoint *p2, QgsPoint *p3, QgsPoint *result)
Calculates the barycentric coordinates of a point (x,y) with respect to p1, p2, p3 and stores the thr...
double ANALYSIS_EXPORT calcCubicHermitePoly(int n, int i, double t)
Calculates the value of a cubic Hermite polynomial.
bool ANALYSIS_EXPORT inCircle(QgsPoint *testp, QgsPoint *p1, QgsPoint *p2, QgsPoint *p3)
Tests, whether 'testp' is inside the circle through 'p1', 'p2' and 'p3'.
void ANALYSIS_EXPORT normalFromPoints(QgsPoint *p1, QgsPoint *p2, QgsPoint *p3, Vector3D *vec)
Calculates the normal vector of the plane through the points p1, p2 and p3 and assigns the result to ...
bool ANALYSIS_EXPORT normalMinDistance(Vector3D *tangent, Vector3D *target, Vector3D *result)
Calculates a Vector orthogonal to 'tangent' with length 1 and closest possible to result....
As part of the API refactoring and improvements which landed in the Processing API was substantially reworked from the x version This was done in order to allow much of the underlying Processing framework to be ported into c
#define QgsDebugError(str)