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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
%CONTENTS GEOM3D Geometry 3D Toolbox.
% Version 1.22 06-Jun-2018 .
%
% Creation, transformations, algorithms and visualization of geometrical
% 3D primitives, such as points, lines, planes, polyhedra, circles and
% spheres.
%
% Euler Angles are defined as follow:
% PHI is the azimut, i.e. the angle of the projection on horizontal plane
% with the Ox axis, with value beween 0 and 180 degrees.
% THETA is the latitude, i.e. the angle with the Oz axis, with value
% between -90 and +90 degrees.
% PSI is the 'roll', i.e. the rotation around the (PHI, THETA) direction,
% with value in degrees
% See also the 'angles3d' page.
%
% Base format for primitives:
% Point: [x0 y0 z0]
% Vector: [dx dy dz]
% Line: [x0 y0 z0 dx dy dz]
% Edge: [x1 y1 z1 x2 y2 z2]
% Plane: [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2]
% Sphere: [x0 y0 z0 R]
% Circle: [x0 y0 z0 R PHI THETA PSI] (origin+center+normal+'roll').
% Ellipsoid: [x0 y0 z0 A B C PHI THETA PSI]
% Cylinder: [X1 Y1 Z1 X2 Y2 Z2 R]
% Box: [xmin xmax ymin ymax zmin zmax]. Used for clipping shapes.
%
% Polygons are represented by N-by-3 array of points, the last point is
% not necessarily the same as the first one. Points must be coplanar.
%
%
% 3D Points
% points3d - Description of functions operating on 3D points.
% midPoint3d - Middle point of two 3D points or of a 3D edge.
% isCoplanar - Tests input points for coplanarity in 3-space.
% transformPoint3d - Transform a point with a 3D affine transform.
% distancePoints3d - Compute euclidean distance between pairs of 3D Points.
% clipPoints3d - Clip a set of points by a box or other 3d shapes.
% drawPoint3d - Draw 3D point on the current axis.
%
% 3D Vectors
% vectors3d - Description of functions operating on 3D vectors.
% transformVector3d - Transform a vector with a 3D affine transform.
% normalizeVector3d - Normalize a 3D vector to have norm equal to 1.
% vectorNorm3d - Norm of a 3D vector or of set of 3D vectors.
% hypot3 - Diagonal length of a cuboidal 3D box .
% crossProduct3d - Vector cross product faster than inbuilt MATLAB cross.
% vectorAngle3d - Angle between two 3D vectors.
% isParallel3d - Check parallelism of two 3D vectors.
% isPerpendicular3d - Check orthogonality of two 3D vectors.
% drawVector3d - Draw vector at a given position.
%
% Angles
% angles3d - Conventions for manipulating angles in 3D.
% anglePoints3d - Compute angle between three 3D points.
% sphericalAngle - Compute angle between points on the sphere.
% angleSort3d - Sort 3D coplanar points according to their angles in plane.
% randomAngle3d - Return a 3D angle uniformly distributed on unit sphere.
%
% Coordinate transforms
% sph2cart2 - Convert spherical coordinates to cartesian coordinates.
% cart2sph2 - Convert cartesian coordinates to spherical coordinates.
% cart2sph2d - Convert cartesian coordinates to spherical coordinates in degrees.
% sph2cart2d - Convert spherical coordinates to cartesian coordinates in degrees.
% cart2cyl - Convert cartesian to cylindrical coordinates.
% cyl2cart - Convert cylindrical to cartesian coordinates.
%
% 3D Lines and Edges
% lines3d - Description of functions operating on 3D lines.
% createLine3d - Create a line with various inputs.
% createEdge3d - Create an edge between two 3D points, or from a 3D line.
% fitLine3d - Fit a 3D line to a set of points.
% parallelLine3d - Create 3D line parallel to another one.
% projPointOnLine3d - Project a 3D point orthogonally onto a 3D line.
% distancePointLine3d - Euclidean distance between 3D point and line.
% isPointOnLine3d - Test if a 3D point belongs to a 3D line.
% linePosition3d - Return the position of a 3D point projected on a 3D line.
% distanceLines3d - Minimal distance between two 3D lines.
% transformLine3d - Transform a 3D line with a 3D affine transform.
% reverseLine3d - Return same 3D line but with opposite orientation.
% normalizeLine3d - Normalizes the direction vector of a 3D line.
% clipLine3d - Clip a line with a box and return an edge.
% drawLine3d - Draw a 3D line clipped by the current axes.
%
% 3D Edges and Rays
% edges3d - Description of functions operating on 3D edges.
% edgeLength3d - Return the length of a 3D edge.
% clipEdge3d - Clip a 3D edge with a cuboid box.
% lineToEdge3d - Convert a 3D straight line to a 3D finite edge.
% edgeToLine3d - Convert a 3D edge to a 3D straight line.
% distancePointEdge3d - Minimum distance between a 3D point and a 3D edge.
% isPointOnEdge3d - Test if a 3D point belongs to an edge.
% drawEdge3d - Draw 3D edge in the current axes.
% createRay3d - Create a 3D ray.
% clipRay3d - Clip a 3D ray with a box and return a 3D edge.
% drawRay3d - Draw a 3D ray on the current axis.
%
% Planes
% planes3d - Description of functions operating on 3D planes.
% createPlane - Create a plane in parametrized form.
% clipPlane - Compute the 3D polygon representing a clipped plane.
% fitPlane - Fit a 3D plane to a set of points.
% normalizePlane - Normalize parametric representation of a plane.
% parallelPlane - Parallel to a plane through a point or at a given distance.
% reversePlane - Return same 3D plane but with opposite orientation.
% isPlane - Check if input is a plane.
% transformPlane3d - Transform a 3D plane with a 3D affine transform.
% planesBisector - Bisector plane between two other planes.
% projPointOnPlane - Return the orthogonal projection of a point on a plane.
% intersectPlanes - Return intersection line between 2 planes in space.
% intersectThreePlanes - Return intersection point between 3 planes in space.
% intersectLinePlane - Intersection point between a 3D line and a plane.
% intersectEdgePlane - Return intersection point between a plane and a edge.
% distancePointPlane - Signed distance betwen 3D point and plane.
% projLineOnPlane - Return the orthogonal projection of a line on a plane.
% isBelowPlane - Test whether a point is below or above a plane.
% medianPlane - Create a plane in the middle of 2 points.
% planeNormal - Compute the normal to a plane.
% planePosition - Compute position of a point on a plane.
% planePoint - Compute 3D position of a point in a plane.
% dihedralAngle - Compute dihedral angle between 2 planes.
% drawPlane3d - Draw a plane clipped by the current axes.
%
% 3D Polygons and curves
% polygons3d - Description of functions operating on 3D polygons.
% isPolygon3d - Check if input is a 3d polygon.
% polygonCentroid3d - Centroid (or center of mass) of a polygon.
% polygonArea3d - Area of a 3D polygon.
% polygon3dNormalAngle - Normal angle at a vertex of the 3D polygon.
% intersectEdgePolygon3d - Intersection point of a 3D edge segment and a 3D polygon.
% intersectLinePolygon3d - Intersection point of a 3D line and a 3D polygon.
% intersectRayPolygon3d - Intersection point of a 3D ray and a 3D polygon.
% clipPolygonByPlane3d - Clip a 3D polygon with a plane.
% drawPolygon3d - Draw a 3D polygon specified by a list of vertex coords.
% drawPolyline3d - Draw a 3D polyline specified by a list of vertex coords.
% fillPolygon3d - Fill a 3D polygon specified by a list of vertex coords.
% transformPolygon3d - Transform a polygon with a 3D affine transform.
%
% 3D Triangles
% triangleArea3d - Area of a 3D triangle.
% distancePointTriangle3d - Minimum distance between a 3D point and a 3D triangle.
% intersectLineTriangle3d - Intersection point of a 3D line and a 3D triangle.
%
% 3D circles and ellipses
% circles3d - Description of functions operating on 3D circles.
% fitCircle3d - Fit a 3D circle to a set of points.
% fitEllipse3d - Fit an ellipse to a set of points.
% circle3dPosition - Return the angular position of a point on a 3D circle.
% circle3dPoint - Coordinates of a point on a 3D circle from its position.
% circle3dOrigin - Return the first point of a 3D circle.
% distancePointCircle3d - Distance between 3D points and 3D circle.
% drawCircle3d - Draw a 3D circle.
% drawCircleArc3d - Draw a 3D circle arc.
% drawEllipse3d - Draw a 3D ellipse.
% projPointOnCircle3d - Project a 3D point onto a 3D circle.
% transformCircle3d - Transform a 3D circle with a 3D affine transformation.
%
% Spheres
% spheres - Description of functions operating on 3D spheres.
% createSphere - Create a sphere containing 4 points.
% fitSphere - Fit a sphere to 3D points using the least squares approach.
% intersectLineSphere - Return intersection points between a line and a sphere.
% intersectPlaneSphere - Return intersection circle between a plane and a sphere.
% drawSphere - Draw a sphere as a mesh.
% drawSphericalEdge - Draw an edge on the surface of a sphere.
% drawSphericalTriangle - Draw a triangle on a sphere.
% fillSphericalTriangle - Fill a triangle on a sphere.
% drawSphericalPolygon - Draw a spherical polygon.
% fillSphericalPolygon - Fill a spherical polygon.
% sphericalVoronoiDomain - Compute a spherical voronoi domain.
%
% Smooth surfaces
% equivalentEllipsoid - Equivalent ellipsoid of a set of 3D points.
% isPointInEllipsoid - Check if a point is located inside a 3D ellipsoid.
% ellipsoidSurfaceArea - Approximated surface area of an ellipsoid.
% oblateSurfaceArea - Approximated surface area of an oblate ellipsoid.
% prolateSurfaceArea - Approximated surface area of a prolate ellipsoid.
% cylinderSurfaceArea - Surface area of a cylinder.
% geodesicCylinder - Computes the geodesic between two points on a cylinder.
% intersectLineCylinder - Compute intersection points between a line and a cylinder.
% projPointOnCylinder - Project a 3D point onto a cylinder.
% revolutionSurface - Create a surface of revolution from a planar curve.
% surfaceCurvature - Curvature on a surface from angle and principal curvatures.
% drawEllipsoid - Draw a 3D ellipsoid.
% drawTorus - Draw a torus (3D ring).
% drawCylinder - Draw a cylinder.
% drawEllipseCylinder - Draw a cylinder with ellipse cross-section.
% drawCapsule - Draw a capsule.
% drawDome - Draw a dome (half-sphere, semi-sphere) as a mesh.
% drawSurfPatch - Draw a 3D surface patch, with 2 parametrized surfaces.
%
% Bounding boxes management
% boxes3d - Description of functions operating on 3D boxes.
% boundingBox3d - Bounding box of a set of 3D points.
% orientedBox3d - Object-oriented bounding box of a set of 3D points.
% intersectBoxes3d - Intersection of two 3D bounding boxes.
% mergeBoxes3d - Merge 3D boxes, by computing their greatest extent.
% box3dVolume - Volume of a 3-dimensional box.
% randomPointInBox3d - Generate random point(s) within a 3D box.
% drawBox3d - Draw a 3D box defined by coordinate extents.
%
% Geometric transforms
% transforms3d - Conventions for manipulating 3D affine transforms.
% fitAffineTransform3d - Compute the affine transform that best register two 3D point sets.
% registerPoints3dAffine - Fit 3D affine transform using iterative algorithm.
% createTranslation3d - Create the 4x4 matrix of a 3D translation.
% createScaling3d - Create the 4x4 matrix of a 3D scaling.
% createRotationOx - Create the 4x4 matrix of a 3D rotation around x-axis.
% createRotationOy - Create the 4x4 matrix of a 3D rotation around y-axis.
% createRotationOz - Create the 4x4 matrix of a 3D rotation around z-axis.
% createBasisTransform3d - Compute matrix for transforming a basis into another basis.
% eulerAnglesToRotation3d - Convert 3D Euler angles to 3D rotation matrix.
% isTransform3d - Check if input is a affine transformation matrix.
% rotation3dToEulerAngles - Extract Euler angles from a rotation matrix.
% createRotation3dLineAngle - Create rotation around a line by an angle theta.
% rotation3dAxisAndAngle - Determine axis and angle of a 3D rotation matrix.
% createRotationVector3d - Calculates the rotation between two vectors.
% createRotationVectorPoint3d - Calculates the rotation between two vectors.
% createRotationAboutPoint3d - Rotate about a point using a rotation matrix.
% recenterTransform3d - Change the fixed point of an affine 3D transform.
% composeTransforms3d - Concatenate several space transformations.
%
% Various drawing Functions
% drawGrid3d - Draw a 3D grid on the current axis.
% drawAxis3d - Draw a coordinate system and an origin.
% drawAxisCube - Draw a colored cube representing axis orientation.
% drawCube - Draw a 3D centered cube, eventually rotated.
% drawCuboid - Draw a 3D cuboid, eventually rotated.
% drawPlatform - Draw a rectangular platform with a given size.
% drawLabels3d - Draw text labels at specified 3D positions.
% drawArrow3d - plot a quiver of 3D arrows.
% drawAngleBetweenVectors3d - Draw an arc between 2 vectors.
%
%
% Credits:
% * Several functions contributed by Sven Holcombe
% * function isCoplanar was originally written by Brett Shoelson.
% * Songbai Ji enhanced file intersectPlaneLine (6/23/2006).
% * several functions contributed by oqilipo
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-11-07
% Copyright 2005-2023 INRA
help(mfilename);
% In development:
% drawPartialPatch - draw surface patch, with 2 parametrized surfaces.
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