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geom3d
David Legland edited this page Dec 1, 2017
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The geom3d module of the MatGeom library provides functions for the creation, processing, transformation, and visualization of geometrical 3D primitives, such as points, lines, planes, polyhedra, circles and spheres. Specific functions for the manipulation of 3D polygonal meshes are located in the meshes3d module.
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.
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.
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
drawPoint3d - Draw 3D point on the current axis.
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
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
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
lines3d - Description of functions operating on 3D lines
createLine3d - Create a line with various inputs.
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
distancePointEdge3d - Minimum distance between a 3D point and a 3D edge
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
midPoint3d - Middle point of two 3D points or of a 3D edge
clipLine3d - Clip a line with a box and return an edge
drawEdge3d - Draw 3D edge in the current Window
drawLine3d - Draw a 3D line on the current axis
planes3d - Description of functions operating on 3D planes
createPlane - Create a plane in parametrized form
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
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
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
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 in the current window
polygons3d - Description of functions operating on 3D polygons
polygonCentroid3d - Centroid (or center of mass) of a polygon
polygonArea3d - Area of a 3D polygon
triangleArea3d - Area of a 3D triangle
polygon3dNormalAngle - Normal angle at a vertex of the 3D polygon
intersectLinePolygon3d - Intersection point of a 3D line and a 3D polygon
intersectLineTriangle3d - Intersection point of a 3D line and a 3D triangle
intersectRayPolygon3d - Intersection point of a 3D ray and a 3D polygon
clipConvexPolygon3dHP - Clip a convex 3D polygon with Half-space
drawPolygon3d - Draw a 3D polygon specified by a list of vertices
drawPolyline3d - Draw a 3D polyline specified by a list of vertices
fillPolygon3d - Fill a 3D polygon specified by a list of points
circles3d - Description of functions operating on 3D circles
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
drawCircle3d - Draw a 3D circle
drawCircleArc3d - Draw a 3D circle arc
drawEllipse3d - Draw a 3D ellipse
spheres - Description of functions operating on 3D spheres
createSphere - Create a sphere containing 4 points
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
inertiaEllipsoid - Inertia ellipsoid of a set of 3D points
ellipsoidSurfaceArea - Approximated surface area of an ellipsoid
oblateSurfaceArea - Approximated surface area of an oblate ellipsoid
prolateSurfaceArea - Approximated surface area of a prolate ellipsoid
intersectLineCylinder - Compute intersection points between a line and 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
drawSurfPatch - Draw a 3D surface patch, with 2 parametrized surfaces
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
transforms3d - Conventions for manipulating 3D affine transforms
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
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
recenterTransform3d - Change the fixed point of an affine 3D transform
composeTransforms3d - Concatenate several space transformations
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