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Barycentric Coordinates

Barycentric coordinates define the position of a point within a given triangle. The coordinates for a given point are calculated with:

• maxon::GeometryUtilsInterface::CalculateBarycentricCoordinate() : Returns the UV coordinates for the given point in the given triangle.
• maxon::GeometryUtilsInterface::CalculateBarycentricCoordinate3D() : Returns the UVW coordinates for the given point in the given triangle.

The coordinates within a polygon are calculated with:

• maxon::GeometryUtilsInterface::CalculatePolygonPointST() : Calculates the s/t coordinates for the given point and polygon.

// triangle const maxon::Vector vertexA { 0, 0, 0 }; const maxon::Vector vertexB { 2, 0, 0 }; const maxon::Vector vertexC { 1, 2, 0 };

// point within the triangle const maxon::Vector point { 1, 1, 0 };

// get barycentrix coordinates const maxon::Vector res = maxon::GeometryUtilsInterface::CalculateBarycentricCoordinate3D (point, vertexA, vertexB, vertexC);

• maxon::GeometryUtilsInterface::CalculateMeanValueCoordinatesWeights() : Returns the mean value coordinates weights for the point inside the given outline.

Interpolation

Bilinear interpolation allows to interpolate values in a two dimensional grid:

• maxon::GeometryUtilsInterface::BilinearInterpolate() : Returns the interpolation result for the given s/t coordinates.
• maxon::GeometryUtilsInterface::InverseBilinarInterpolate() : Returns the bilinear coordinates for the given point.
• maxon::GeometryUtilsInterface::InverseBilinarInterpolateNewton() : Returns the bilinear coordinates for the given point with a Newton iteration method.
• maxon::GeometryUtilsInterface::InverseBilinarInterpolate2D() : Returns the bilinear coordinates for the 2D given point.
• maxon::GeometryUtilsInterface::InverseBilinarInterpolate2DNewton() : Returns the bilinear coordinates for the given 2D point with a Newton iteration method.

// color values const maxon::Vector red { 1.0, 0, 0 }; const maxon::Vector green { 0.0, 1.0, 0.0 }; const maxon::Vector blue { 0.0, 0.0, 1.0 }; const maxon::Vector white { 1.0 };

// get bilinear interpolation const maxon::Vector res = maxon::GeometryUtilsInterface::BilinearInterpolate (red, green, blue, white, s, t);

Intersection

These functions allow to calculate the intersection of lines, half-lines, segments, triangles and quads.

Intersection of lines, half-lines, and sections with each other:

• maxon::GeometryUtilsInterface::IntersectsSegments2D(): Checks if the two given 2D segments intersect.
• maxon::GeometryUtilsInterface::SegmentsIntersectionTest2D() : Checks if the two given 2D segments intersect. Faster than the above function.
• maxon::GeometryUtilsInterface::IntersectSegments() : Checks if the two given 3D segments intersect.
• maxon::GeometryUtilsInterface::IntersectLineSegment() : Checks if the given line intersects the given segment.
• maxon::GeometryUtilsInterface::IntersectLineHalfLine() : Checks if the given line intersects the given half-line.
• maxon::GeometryUtilsInterface::IntersectLines() : Checks if the two given lines intersect.
• maxon::GeometryUtilsInterface::IntersectHalfLines() : Checks if the two given half-lines intersect.
• maxon::GeometryUtilsInterface::IntersectHalfLineSegment() : Checks if the given half-line and segment intersect.

See also:

• maxon::GeometryUtilsInterface::LineLineDistance() : Returns the distance of the two given lines.

// check segment intersection maxon::Vector segIntersectPoint { maxon::DONT_INITIALIZE }; const maxon::Bool segementIntersection = maxon::GeometryUtilsInterface::IntersectSegments (pointA, pointB, pointC, pointD, segIntersectPoint); if (segementIntersection) DiagnosticOutput ( "Segments intersect at @" , segIntersectPoint);

// check line intersection maxon::Vector lineIntersectPoint { maxon::DONT_INITIALIZE }; const maxon::Bool lineIntersection = maxon::GeometryUtilsInterface::IntersectLines (pointA, pointB, pointC, pointD, lineIntersectPoint); if (lineIntersection) DiagnosticOutput ( "Line intersection at @" , lineIntersectPoint);

Intersection of lines, half-lines, and segments with planes:

• maxon::GeometryUtilsInterface::IntersectLinePlane() : Checks if the given lines intersects the given plane.
• maxon::GeometryUtilsInterface::IntersectSegmentPlane() : Checks if the given segment intersects the given plane.
• maxon::GeometryUtilsInterface::IntersectHalfLinePlane() : Checks if the given half-line intersects the given plane.

// check line/plane intersection maxon::Vector linePlaneIntersectionPoint { maxon::DONT_INITIALIZE }; const maxon::Bool linePlaneIntersect = maxon::GeometryUtilsInterface::IntersectLinePlane (startPoint, lineDir, planePoint, planeNormal, linePlaneIntersectionPoint); if (linePlaneIntersect) DiagnosticOutput ( "Line intersects plane at @" , linePlaneIntersectionPoint);

// check half-line/plane intersection maxon::Vector halfLinePlaneIntersectPoint { maxon::DONT_INITIALIZE }; const maxon::Bool halfLinePlaneIntersect = maxon::GeometryUtilsInterface::IntersectHalfLinePlane (startPoint, lineDir, planePoint, planeNormal, halfLinePlaneIntersectPoint); if (halfLinePlaneIntersect) DiagnosticOutput ( "Half-line intersects plane at @" , halfLinePlaneIntersectPoint);

// check segment/plane intersection maxon::Vector segmentPlaneIntersectPoint { maxon::DONT_INITIALIZE }; const maxon::Bool segmentPlaneIntersect = maxon::GeometryUtilsInterface::IntersectSegmentPlane (startPoint, endPoint, planePoint, planeNormal, segmentPlaneIntersectPoint); if (segmentPlaneIntersect) DiagnosticOutput ( "Segments intersects plane at @" , segmentPlaneIntersectPoint);

Intersections of lines, half-lines and segments with triangles and quadrangles:

• maxon::GeometryUtilsInterface::IntersectLineTriangle() : Checks if the given line intersects the given triangle.
• maxon::GeometryUtilsInterface::IntersectHalfLineTriangle() : Checks if the given half-line intersects the given triangle.
• maxon::GeometryUtilsInterface::IntersectSegmentTriangle() : Checks if the given segment intersects the given triangle.
• maxon::GeometryUtilsInterface::IntersectLineQuadrangle() : Checks if the given line intersects the given quadrangle.
• maxon::GeometryUtilsInterface::IntersectHalfLineQuadrangle() : Checks if the given half-line intersects the given quadrangle.

// check line/triangle intersection maxon::Vector lineTriIntersectPoint { maxon::DONT_INITIALIZE }; const maxon::Bool lineTriIntersect = maxon::GeometryUtilsInterface::IntersectLineTriangle (startPoint, lineDir, pointA, pointB, pointC, lineTriIntersectPoint); if (lineTriIntersect) DiagnosticOutput ( "Line intersects with triangle at @" , lineTriIntersectPoint);

// check half-line/triangle intersection maxon::Vector halfLineTriIntersectPoint { maxon::DONT_INITIALIZE }; const maxon::Bool halfLineTriIntersect = maxon::GeometryUtilsInterface::IntersectHalfLineTriangle (startPoint, lineDir, pointA, pointB, pointC, halfLineTriIntersectPoint); if (halfLineTriIntersect) DiagnosticOutput ( "Half-line intersects triangle at @" , halfLineTriIntersectPoint);

// check segment/triangle intersection maxon::Vector segmentTriIntersectPoint { maxon::DONT_INITIALIZE }; const maxon::Bool segmentTriIntersect = maxon::GeometryUtilsInterface::IntersectSegmentTriangle (startPoint, endPoint, pointA, pointB, pointC, segmentTriIntersectPoint); if (segmentTriIntersect) DiagnosticOutput ( "Segment intersects triangle at @" , segmentTriIntersectPoint);

Intersection of triangles, quadrangles and planes:

• maxon::GeometryUtilsInterface::IntersectPlanes() : Checks if the two given planes intersect.
• maxon::GeometryUtilsInterface::TrianglesIntersectionTest() : Checks if the two given triangles intersect.

Points Inside

These functions are used to check if a given point is inside a given shape:

• maxon::GeometryUtilsInterface::PointInOutline2D() : Checks if the given point is within the shape defined by the given points.
• maxon::GeometryUtilsInterface::PointInTriangle() : Checks if the given point is inside the given triangle.
• maxon::GeometryUtilsInterface::PointInTriangle2D() : Checks if the given point is inside the given 2D triangle.
• maxon::GeometryUtilsInterface::GetPointInPolygonWindingNumber2D() : Returns the winding number for the given point and shape.
• maxon::GeometryUtilsInterface::GetPointInPolygonWindingNumber2DExact() : Returns the winding number for the given 2D point and shape. Exact yet slower version.
• maxon::GeometryUtilsInterface::GetPointInPolygonWindingNumber() : Returns the winding number for the given point and shape.

// point within the triangle const maxon::Vector2d point { 0.5, 0.25 };

// check if inside the triangle const maxon::Bool inside = maxon::GeometryUtilsInterface::PointInTriangle2D (point, points[0], points[1], points[2]); // calculate winding number const maxon::Int windingNumber = maxon::GeometryUtilsInterface::GetPointInPolygonWindingNumber2D (point, points);

Points on Lines

These functions check if a given point is on a line, half-line or within a segment:

• maxon::GeometryUtilsInterface::PointInHalfLine() : Checks if the given point is on the given half-line.
• maxon::GeometryUtilsInterface::PointInSegment2D() : Checks if the given point is one the given 2D segment.
• maxon::GeometryUtilsInterface::PointInSegment() : Checks if the given point is one the given segment.
• maxon::GeometryUtilsInterface::InterpolatePointOnSegment() : Returns the linear interpolation value for the given point and given segment.
• maxon::GeometryUtilsInterface::InterpolatePointOnSegment2D() : Returns the linear interpolation value for the given 2D point and segment.

// get direction vector const maxon::Vector direction = maxon::Vector (segmentEnd - segmentStart). GetNormalized ();

// check on half-line const maxon::Bool pointInHalfLine = maxon::GeometryUtilsInterface::PointInHalfLine (point, segmentStart, direction);

// check on segment const maxon::Bool pointInSegment = maxon::GeometryUtilsInterface::PointInSegment (point, segmentStart, segmentEnd);

// position const maxon::Float value = maxon::GeometryUtilsInterface::InterpolatePointOnSegment (segmentStart, segmentEnd, point, false );

Circumcenter

The circumcenter is the center of a circle containing all points of the given shape.

• maxon::GeometryUtilsInterface::CalculateCircumcenter() : Calculates the circumcenter and radius for the given triangle.
• maxon::GeometryUtilsInterface::CalculateCircumcenter2D() : Calculates the circumcenter and radius for the given 2D triangle.

Vertex Properties

The convexity of a given vertex can be checked with:

• maxon::GeometryUtilsInterface::IsVertexConvex() : Checks the convexity for the given 3D points.
• maxon::GeometryUtilsInterface::IsVertexConvex2D() : Checks the convexity for the given 2D points.

另请参阅 ConvexHull Manual .

Projection

Functions to project points:

• maxon::GeometryUtilsInterface::Points3Dto2D() : Projects 3D points on a given plane.
• maxon::GeometryUtilsInterface::Point2Dto3D() : Returns a 3D point from 2D coordinates.
• maxon::GeometryUtilsInterface::Points2Dto3D() : Calculates 3D points from the given 2D points.

杂项

Miscellaneous functions are:

• maxon::GeometryUtilsInterface::CalculateBestFitPlane() : Calculates the best plane for the given points.
• maxon::GeometryUtilsInterface::CalculateOutlineNormal() : Returns the normal vector of a n-gon outline.
• maxon::GeometryUtilsInterface::LinearRemapToRange() : Remaps a value from one range to another range.

// change range of values const maxon::Float sourceMin = 0.0; const maxon::Float sourceMax = 10.0; const maxon::Float destMin = 0.0; const maxon::Float destMax = 1.0; for ( maxon::Vector2d & point : points) { point.x = maxon::GeometryUtilsInterface::LinearRemapToRange (point.x, sourceMin, sourceMax, destMin, destMax); point.y = maxon::GeometryUtilsInterface::LinearRemapToRange (point.y, sourceMin, sourceMax, destMin, destMax); }

// find circumcenter maxon::Vector2d center; maxon::Float radius; const maxon::Bool res = maxon::GeometryUtilsInterface::CalculateCircumcenter2D (points[0], points[1], points[2], center, radius); if ( MAXON_LIKELY (res)) { ApplicationOutput ( "Center: @, Radius: @" , center, radius); }

延伸阅读

• 建模
• Vectors