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Geometry 3D
Geometry 3D Angle Metrics |
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Icon | Name | Description / Applications | Modules | |
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AngleBetweenLines3D | Measures the smaller and the larger angle between two lines in 3D. |
Vision3DLite | ||
AngleBetweenPlanes | Measures the smaller and the larger angle between two planes in 3D. |
Vision3DLite | ||
AngleBetweenSegments3D | Measures the angle between two segments in 3D. |
Vision3DLite | ||
AngleBetweenThreePoints3D | Measures the angle defined by three consecutive points in 3D. |
Vision3DLite | ||
AngleBetweenVectors3D | Measures the angle between two vectors in 3D. |
Vision3DLite | ||
Geometry 3D Basics |
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Icon | Name | Description / Applications | Modules | |
CreateBox3D | Creates a box in 3D. |
Vision3DLite | ||
CreateSegment3D | Produces a segment in 3D of given parameters. |
Vision3DLite | ||
LoadPoint3DArrayFromTextFile | Loads arrays of 3D points from text file. |
Vision3DLite | ||
RandomPoint3D | Creates random 3D point inside given box. |
Vision3DLite | ||
SkipEmptyBox3D | If the input box in 3D has all dimensions different from zero, then it is copied to the output; otherwise Nil is returned. Secures against domain errors caused by empty boxes. |
Vision3DLite | ||
TestBox3DEmpty | Tests whether the box in 3D is empty. |
Vision3DLite | ||
TestBox3DInBox3D | Tests whether a box in 3D is contained in another one. |
Vision3DLite | ||
TestBox3DIntersectsWith | Tests whether two boxes in 3D have non-empty intersection. |
Vision3DLite | ||
TestBox3DNotEmpty | Tests whether the box in 3D is not empty. |
Vision3DLite | ||
Geometry 3D Constructions |
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Icon | Name | Description / Applications | Modules | |
CircleThroughPoints3D | Computes a circle in 3D passing through three noncollinear 3D points. |
Vision3DLite | ||
LineThroughPoint3D | Computes a line in 3D passing through a point with given direction. |
Vision3DLite | ||
LineThroughPoints3D | Computes a line in 3D passing through two points. |
Vision3DLite | ||
PlaneThroughLineAndPoint3D | Computes a plane passing through a line and a point in 3D. |
Vision3DLite | ||
PlaneThroughPoints3D | Computes a plane passing through three distinct points in 3D. |
Vision3DLite | ||
ProjectPointsOnLine3D | Projects points onto a line. |
Vision3DLite | ||
VectorBetweenPoints3D | Computes a vector representing distance from one point in 3D to another. |
Vision3DLite | ||
Geometry 3D Distance Metrics |
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Icon | Name | Description / Applications | Modules | |
CircleToPlaneDistance3D | Measures the distance between a circle in 3D and a plane. |
Vision3DLite | ||
LineToLineDistance3D | Measures the distance between two lines in 3D. |
Vision3DLite | ||
PointSequenceDistances3D | Measures the distances between consecutive points of a point sequence in 3D. |
Vision3DLite | ||
PointToCircleDistance3D | Measures the distance between a 3D point and a circle in 3D. |
Vision3DLite | ||
PointToLineDistance3D | Measures the distance between a 3D point and a line in 3D. |
Vision3DLite | ||
PointToPlaneDistance3D | Measures the distance between a 3D point and a plane. |
Vision3DLite | ||
PointToPointDistance3D | Measures the distance between two 3D points. |
Vision3DLite | ||
PointToSegmentDistance3D | Measures the distance between a 3D point and a segment in 3D. |
Vision3DLite | ||
SegmentToPlaneDistance3D | Measures the distance between a segment in 3D and a plane. |
Vision3DLite | ||
SegmentToSegmentDistance3D | Measures the distance between two segments in 3D. |
Vision3DLite | ||
Geometry 3D Features |
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Icon | Name | Description / Applications | Modules | |
Box3DCenter | Returns the center of the input box in 3D. |
Vision3DLite | ||
Box3DCharacteristicPoint | Returns a characteristic point of a box in 3D. |
Vision3DLite | ||
Box3DSurfaceArea | Returns the surface area of the input box in 3D. |
Vision3DLite | ||
Box3DVolume | Returns the volume of the input box in 3D. |
Vision3DLite | ||
Boxes3DBoundingBox3D_OrNil | Computes the bounding box 3D of given boxes in 3D; returns NIL if the array is empty. |
Vision3DLite | ||
BoxesBoundingBox3D | Computes the bounding box 3D of given boxes in 3D. |
Vision3DLite | ||
Circle3DArea | Computes the area of a circle in 3D. |
Vision3DLite | ||
Circle3DBoundingBox | Computes the smallest box in 3D containing a circle in 3D. |
Vision3DLite | ||
Circle3DPerimeterLength | Computes the length of a circle in 3D perimeter. |
Vision3DLite | ||
Plane3DNormalVector | Computes the normal vector of a line. |
Vision3DLite | ||
Plane3DOrientation | Computes the orientation of a plane as angles in the range from 0 to 180 between the plane and coordinate planes. |
Vision3DLite | ||
Points3DMedian | Computes the geometric median of the input points. |
Vision3DLite | ||
PointsBoundingBox3D | Computes the smallest box in 3D containing an array of points in 3D. |
Vision3DLite | ||
PointsBoundingBox3D_OrNil | Computes the smallest box in 3D containing an array of points in 3D; returns NIL if the array is empty. |
Vision3DLite | ||
PointsMassCenter3D | Computes the central point of the input points. |
Vision3DLite | ||
Segment3DBisector | Computes a plane passing through the center of a segment in 3D at a right angle. |
Vision3DLite | ||
Segment3DBoundingBox | Computes the smallest box in 3D containing a segment in 3D. |
Vision3DLite | ||
Segment3DCenter | Computes the center point of a segment in 3D. |
Vision3DLite | ||
Segment3DLength | Computes the length of a segment in 3D. |
Vision3DLite | ||
Segment3DLine | Computes the line in 3D passing through a segment. |
Vision3DLite | ||
Segment3DVector | Returns the vector [x2 - x1, y2 - y1, z2 - z1]. |
Vision3DLite | ||
Vector3DAzimuth | Computes the angle between a 3D vector's projection to the XY plane and the X axis measured toward Y axis, as an angle in the range from 0 to 360. |
Vision3DLite | ||
Vector3DElevation | Computes the angle between a 3D vector's projection to the XY plane and itself measured toward Z axis, as an angle in the range from -90 to 90. |
Vision3DLite | ||
Vector3DLength | Computes the length of a 3D vector. |
Vision3DLite | ||
Vectors3DMedian | Computes the geometric median of the input vectors. |
Vision3DLite | ||
Geometry 3D Fitting |
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Icon | Name | Description / Applications | Modules | |
AnalyzePoint3DGrid | Analyzes the steps in X and Y directions of a point 3D grid. |
Vision3DLite | ||
FitCircle3DToHole | Fits a circle to a hole in a plane. |
Vision3DLite | ||
FitCircleToPoints3D | Approximates points in 3D with a circle using selected outliers suppression method. |
Vision3DStandard | ||
FitLineToPoints3D | Approximates points in 3D with a line using the Least Squares method. |
Vision3DStandard | ||
FitLineToPoints3D_LTE | Approximates points in 3D with a line using Least Trimmed Error algorithm. |
Vision3DStandard | ||
FitLineToPoints3D_M | Approximates points in 3D with a line using selected M-estimator for outlier suppression. Finding a locally optimal line in 3D. Good enough when the number of outliers is small. |
Vision3DStandard | ||
FitLineToPoints3D_RANSAC | Approximates points in 3D with a line using a RANSAC algorithm. |
Vision3DStandard | ||
FitPlaneToPoints | Approximates points with a plane using the Least Squares method. |
Vision3DStandard | ||
FitPlaneToPoints_M | Approximates points with a plane using selected M-estimator for outlier suppression. Finding a locally optimal plane. Good enough when the number of outliers is small. |
Vision3DStandard | ||
FitSegmentToPoints3D | Approximates points in 3D with a segment using selected outliers suppression method. |
Vision3DStandard | ||
FitSegmentToPoints3D_LTE | Approximates points in 3D with a segment using a RANSAC algorithm. |
Vision3DStandard | ||
FitSegmentToPoints3D_RANSAC | Approximates points in 3D with a segment using a RANSAC algorithm. |
Vision3DStandard | ||
Geometry 3D Interpolations |
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Icon | Name | Description / Applications | Modules | |
LerpPoints3D | Linearly interpolates between two points in 3D. |
Vision3DStandard | ||
LerpSegments3D | Linearly interpolates between two segments in 3D. |
Vision3DStandard | ||
LerpVectors3D | Linearly interpolates between two 3D vectors. |
Vision3DStandard | ||
Geometry 3D Intersections |
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Icon | Name | Description / Applications | Modules | |
BoxIntersection3D | Computes the common part of two boxes in 3D. |
Vision3DLite | ||
CirclePlaneIntersection3D | Computes common points of a circle in 3D and a plane. |
Vision3DLite | ||
LineLineIntersection3D | Computes a common point of two lines in 3D. |
Vision3DLite | ||
LinePlaneIntersection3D | Computes the intersection point of a line in 3D and a plane. |
Vision3DLite | ||
PlanePlaneIntersection3D | Computes a common line in 3D of two planes. |
Vision3DLite | ||
SegmentPlaneIntersection3D | Computes the intersection point of a segment in 3D and a plane. |
Vision3DLite | ||
Geometry 3D Normalizations |
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Icon | Name | Description / Applications | Modules | |
RemoveInvalidPoints3D | Removes invalid 3D points from an array (i.e. points with NaN or INF coordinates). |
Vision3DLite | ||
Geometry 3D Relations |
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Icon | Name | Description / Applications | Modules | |
TestLine3DThroughCircle3D | Tests whether a line in 3D goes through a circle in 3D. |
Vision3DLite | ||
TestPoint3DInBox3D | Tests whether a point in 3D lies in a box in 3D. |
Vision3DLite | ||
Geometry 3D Spatial Transforms |
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Icon | Name | Description / Applications | Modules | |
AlignPoint3DArrayToPlane | Rotates an array of 3D points with a rotation that transforms the input plane to be parallel to XY plane. |
Vision3DLite | ||
Box2DToBox3D_AxesPlane | Projects a 2D box onto a plane defined by 3D coordinate axes. |
Vision3DLite | ||
Box3DToBox2D_AxesPlane | Projects a 3D box onto a plane defined by coordinate axes. |
Vision3DLite | ||
Circle2DToCircle3D_AxesPlane | Projects a 2D circle onto a plane defined by 3D coordinate axes. |
Vision3DLite | ||
Circle3DToCircle2D_AxesPlane | Projects a 3D circle onto a plane defined by coordinate axes. |
Vision3DLite | ||
Line2DToLine3D_AxesPlane | Projects a 2D line onto a plane defined by 3D coordinate axes. |
Vision3DLite | ||
Line3DToLine2D_AxesPlane | Projects a 3D line onto a plane defined by coordinate axes. |
Vision3DLite | ||
MirrorPoint3D | Mirrors a point according to the input plane. |
Vision3DLite | ||
MirrorPoint3DArray | Mirrors each point from the array according to the input plane. |
Vision3DLite | ||
Point2DToPoint3D_AxesPlane | Projects a 2D point onto a plane defined by 3D coordinate axes. |
Vision3DLite | ||
Point3DToPoint2D_AxesPlane | Projects a 3D point onto a plane defined by coordinate axes. |
Vision3DLite | ||
Points2DToPoints3D_AxesPlane | Projects an array of 2D points onto a plane defined by 3D coordinate axes. |
Vision3DLite | ||
Points3DToPoints2D_AxesPlane | Projects an array of 3D points onto a plane defined by coordinate axes. |
Vision3DLite | ||
ProjectLineOntoPlane3D | Projects a line 3D onto a plane. |
Vision3DLite | ||
ProjectPoint2DOntoPlane3D | Projects a point on a plane Z=0 onto a given plane, translating it parallel to Z axis. |
Vision3DLite | ||
ProjectPointOnLine3D | Projects a point 3D onto a line in 3D. |
Vision3DLite | ||
ProjectPointOntoPlane3D | Projects a point 3D onto a plane. |
Vision3DLite | ||
ProjectPointOrthogonal | Converts a point through a simple orthogonal projection, parallel to the Z axis. |
Vision3DLite | ||
ProjectPointPerspective | Converts a point through a perspective projection, parallel to the Z axis. |
Vision3DLite | ||
RescaleBox3D | Changes the distances of box in 3D to a reference point. |
Vision3DLite | ||
RescaleCircle3D | Changes radius of a circle in 3D and translates its center in relation to a reference point. |
Vision3DLite | ||
RescaleLine3D | Changes the input line in 3D distance to a reference point. |
Vision3DLite | ||
RescalePlane | Changes the input plane distance to a reference point. |
Vision3DLite | ||
RescalePoint3D | Changes the distance of a point to a reference point. |
Vision3DLite | ||
RescalePoint3DArray | Changes the distances of array points to a reference point. |
Vision3DLite | ||
RescaleSegment3D | Lengthens or shortens a segment in 3D relatively. |
Vision3DLite | ||
RescaleVector3D | Lengthens or shortens a 3D vector relatively preserving its direction. |
Vision3DLite | ||
ResizeBox3D | Changes the dimensions of a box in 3D. |
Vision3DLite | ||
ResizeBox3D_Delta | Changes the dimensions of a box in 3D by adding some values. |
Vision3DLite | ||
ResizeBox3D_Relative | Resizes a box in 3D to relatively defined dimensions. |
Vision3DLite | ||
ResizeCircle3D | Changes radius of a circle in 3D. |
Vision3DLite | ||
ResizeCircle3D_Delta | Changes radius of a circle in 3D by adding a value. |
Vision3DLite | ||
ResizeSegment3D | Lengthens or shortens a segment in 3D to a new length preserving its orientation and center point. |
Vision3DLite | ||
ResizeSegment3D_Delta | Changes length of a segment in 3D by adding a value preserving its orientation and center point. |
Vision3DLite | ||
ResizeVector3D | Lengthens or shortens a 3D vector preserving its direction. |
Vision3DLite | ||
ResizeVector3D_Delta | Extends length of a 3D vector by adding a value preserving its direction. |
Vision3DLite | ||
ReverseSegment3D | Swaps the two endpoints of a segment in 3D. |
Vision3DLite | ||
RotateCircle3D | Rotates a circle in 3D around an axis in 3D. |
Vision3DLite | ||
RotateCircle3D_AroundSegment | Rotates a circle in 3D around a segment (the axis) in 3D. |
Vision3DLite | ||
RotateLine3D | Rotates a line in 3D around an axis in 3D. |
Vision3DLite | ||
RotateLine3D_AroundSegment | Rotates a line in 3D around a segment (the axis) in 3D. |
Vision3DLite | ||
RotatePlane | Rotates a plane in 3D around an axis in 3D. |
Vision3DLite | ||
RotatePlane_AroundSegment | Rotates a plane in 3D around a segment (the axis) in 3D. |
Vision3DLite | ||
RotatePoint3D | Rotates a 3D point around an axis in 3D. |
Vision3DLite | ||
RotatePoint3DArray | Rotates an array of 3D points around an axis in 3D. |
Vision3DLite | ||
RotatePoint3DArray_AroundSegment | Rotates an array of 3D points around a segment (the axis). |
Vision3DLite | ||
RotatePoint3D_AroundSegment | Rotates a 3D point around a segment (the axis). |
Vision3DLite | ||
RotateSegment3D | Rotates a segment in 3D around an axis in 3D. |
Vision3DLite | ||
RotateSegment3D_AroundSegment | Rotates a segment in 3D around a segment (the axis) in 3D. |
Vision3DLite | ||
RotateVector3D | Rotates a 3D vector around another 3D vector (the axis). |
Vision3DLite | ||
Segment2DToSegment3D_AxesPlane | Projects a 2D segment onto a plane defined by 3D coordinate axes. |
Vision3DLite | ||
Segment3DToSegment2D_AxesPlane | Projects a 3D segment onto a plane defined by coordinate axes. |
Vision3DLite | ||
Segments2DToSegments3D_AxesPlane | Projects an array of 2D segments onto a plane defined by 3D coordinate axes. |
Vision3DLite | ||
Segments3DToSegments2D_AxesPlane | Projects an array of 3D segments onto a plane defined by coordinate axes. |
Vision3DLite | ||
SplitPointsByPlane | Separates the points being on one side of the input plane from the others. |
Vision3DLite | ||
TransformCircle3D | Applies a general transformation expressed by a matrix to a 3D circle. |
Vision3DLite | ||
TransformLine3D | Applies a general transformation expressed by a matrix to a 3D line. |
Vision3DLite | ||
TransformPlane | Applies a general transformation expressed by a matrix to a plane. |
Vision3DLite | ||
TransformPoint3D | Applies a general transformation expressed by a matrix to a 3D point. |
Vision3DLite | ||
TransformPoint3DArray | Applies a general transformation expressed by a matrix to an array of 3D points. |
Vision3DLite | ||
TransformSegment3D | Applies a general transformation expressed by a matrix to a 3D segment. |
Vision3DLite | ||
TransformVector3D | Applies a general transformation expressed by a matrix to a 3D vector. |
Vision3DLite | ||
TranslateBox3D | Shifts a box in 3D by a vector. |
Vision3DLite | ||
TranslateCircle3D | Shifts a circle in 3D by a vector. |
Vision3DLite | ||
TranslateLine3D | Shifts a line in 3D by a vector. |
Vision3DLite | ||
TranslatePlane | Shifts a plane in 3D by a vector. |
Vision3DLite | ||
TranslatePoint3D | Translates a point by a vector. |
Vision3DLite | ||
TranslatePoint3DArray | Translates an array of points by a vector. |
Vision3DLite | ||
TranslatePoint3D_Toward | Translates a point in 3D towards another point in 3D by a specified distance. |
Vision3DLite | ||
TranslateSegment3D | Shifts a segment in 3D by a vector. |
Vision3DLite | ||
TrimLine3D | Creates a segment contained in a box in 3D from a line in 3D. |
Vision3DLite | ||
TrimPoint3DArray | Removes points not contained in a box in 3D from an array. |
Vision3DLite | ||
TrimSegment3D | Creates a segment contained in a box in 3D from another segment in 3D. |
Vision3DLite | ||
Vector2DToVector3D_AxesPlane | Projects a 2D vector onto a plane defined by 3D coordinate axes. |
Vision3DLite | ||
Vector3DToVector2D_AxesPlane | Projects a 3D vector onto a plane defined by coordinate axes. |
Vision3DLite |