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The geometryutils.h header file contains the maxon::GeometryUtilsInterface which includes various functions to handle vectors, lines, half-lines (rays), line segments and primitives like triangles and quads.

Angles

Angles between vectors can be calculated with:

maxon::GeometryUtilsInterface::GetAngle2D(): Returns the angle between the two given vectors. See also Mathematical Functions.
maxon::GeometryUtilsInterface::CalculateBisector(): Returns the bisector of the two given vectors.

Areas

Multiple points can define a triangle, a quad or an arbitrary shape.

maxon::GeometryUtilsInterface::CalculateTriangleArea(): Returns the area of the given triangle.
maxon::GeometryUtilsInterface::CalculateSignedTriangleArea(): Returns the signed area of the given triangle.
maxon::GeometryUtilsInterface::CalculateQuadrangleArea(): Returns the area of the given quadrangle.
maxon::GeometryUtilsInterface::CalculateOutlineArea(): Returns the unsigned area of an outline,

  // This example calculate the areas of different shapes.
 
  const maxon::Float triArea   = maxon::GeometryUtilsInterface::CalculateTriangleArea(points[0], points[1], points[2]);
  const maxon::Float quadArea  = maxon::GeometryUtilsInterface::CalculateQuadrangleArea(points[0], points[1], points[2], points[3]);
  const maxon::Float shapeArea = maxon::GeometryUtilsInterface::CalculateOutlineArea(points);

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.

  // This example calculates the barycentric coordinates for the given point.
 
  // 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.

  // This example performs bilinear interpolation between the given color values.
 
  // 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.

  // This example checks if the given segments and lines intersect.
 
  // 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.

  // This example checks the intersection of a line, half-line and a segment with a 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.

  // This example checks the intersection of a line, half-line, and segment with a triangle.
 
  // 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.

  // This example tests if the given point is within the given triangle and
  // also calculates the winding number for the given points.
 
  // 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.

  // This example checks if the given point in on the given segment or half line and
  // calculates the position within the 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.

  // This example calculates the circumcenter and radius for the given triangle.
 
  maxon::Vector center;
  maxon::Float  radius { 0 };
 
  const maxon::Bool foundCenter = maxon::GeometryUtilsInterface::CalculateCircumcenter(pointA, pointB, pointC, center, radius);
 
  if (foundCenter)
    DiagnosticOutput("Center at @, Radius: @", center, radius);

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.

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.

Miscellaneous

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.

  // This example remaps the values of the given points
  // and calculates the circumcenter of the resulting triangle.
 
  // 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);
  }

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