## Matlab geom3d函数注释 转

o
osc_ddwjgohl

Matlab geom3d函数解析 geom3d函数库

geom3d库的目的是处理和可视化三维几何原语，如点、线、平面、多面体等。它提供了操作三维几何原语的底层功能，使得开发更复杂的几何算法变得更加容易。 | 序号 | 函数名 | 作用 | 输入 | 输出 | | --- | --- | --- | --- | --- | | 1 | `area = triangleArea3d(pt1, pt2, pt3)` | 获取三角形面积 | 三个点坐标 [10 10 10], [30 10 10], [10 40 10] | 面积 | | 2 | `area = polygonArea3d(poly, varargin)` | 获取三维多边形的面积 | 点的坐标向量poly = [10 30 20;20 30 20;20 40 20;10 40 20] | 面积 | | 3 | `centroid = polygonCentroid3d(varargin)` | 获取三维多边形的中点 | 点坐标 poly = [0 0 0; 10 0 10;10 10 20;0 10 10] | 点坐标 | | 4 | `point = projPointOnPlane(point, plane)` | 点在平面上的正交投影 | 点坐标[ x,y,z]和平面点、两个向量 [X0 Y0 Z0 VX1 VY1 VZ1 VX2 VY2 VZ2] | 点坐标 | | 5 | `[newLine, isOrthogonal] = projLineOnPlane(line, plane)` | 直线在平面上的投影 | 输入为线和平面 | 是否正交 | | 6 | `point = projPointOnLine3d(point, line)` | 点在线上的投影 | 输入为点和线 | 输出为点坐标 | | 7 | `n = planeNormal(plane)` | 计算平面的法向量 | PLANE : [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2] | N : [dx dy dz] | | 8 | ` b = isPointOnLine3d(point, line, varargin)` |** 判断点是否在直线上** | point 和 line | | | 9 | `varargout = angleSort3d(pts, varargin)` | 根据共面点在平面上的角度对其进行排序。| | 10 | `box = boundingBox3d(points)` | 点集的包围盒 | 点集| [xmin xmax ymin ymax zmin zmax] | | 11 | `vol = box3dVolume(box)` | 三维包围盒的体积| | | 12 | `point = circle3dPoint(circle, pos)` | 点在三维圆上的坐标 | | 13 | `theta = circle3dPosition(point, circle)` | 三维点在三维圆上的角度 | | 14 | `poly2 = clipConvexPolygon3dHP(poly, plane)` | 用半空间裁剪一个三维的多边形 | 多边形和平面 |输出为点集 | | 15 | ` clipped = clipEdge3d(edge, box)` | 用长方体修剪三维边 | | 16 | `edge = clipLine3d(line, box)` | 用长方体修剪三维线 | 线和长方体 | 返回边 | | 17 | `poly2 = clipPolygon3dHP(poly, plane)` | 用平面来裁剪三维多边形 | | 18 | `createEdge3d` | 创建一个三维的两点之间的线 | 两个点 | 边 |
| 19 | `createLine3d` | 创建线 | 两个点 | 线 | | 20 | `plane = createPlane(varargin)` | 创建平面 | 输入为三个点 | 平面 | | 21 | `mat = createRotation3dLineAngle(line, theta)` | 围绕一个线旋转一定的角度 | line 和角度 | 矩阵 | | 22 | `trans = createScaling3d(varargin)` | 创建一个4X4的缩放矩阵 | 23 | `trans = createTranslation3d(varargin)` | 创建一个4X4的平移矩阵 | | 24 | `createRotationOx` | | 25 | `createRotationOy` | | 26 | `createRotationOz` | | 27 | `ROT = createRotationVector3d(A,B)` | 计算两个向量 之间的旋转 | | 28 | `TFM = createRotationVectorPoint3d(A,B,P)` | | 29 | `c = crossProduct3d(a,b)` | 叉乘 | | 30 | `varargout = cyl2cart(varargin)` | 柱坐标转换成笛卡尔坐标系 | | 31 | `Surface area of a cylinder.` | 圆柱的表面积 | | 32 | `theta = dihedralAngle(plane1, plane2)` | 计算两个面之间的二面角 | | 33 | `[d, pt1, pt2] = distanceLines3d(line1, line2)` | 计算两条线之间的距离 | | 34 | `[dist, t] = distancePointEdge3d(point, edge)` | 计算点到线的距离 | | 35 | `d = distancePointLine3d(point, line)` | 计算点到线的距离 | | 36 | `d = distancePointPlane(point, plane)` | 计算点到面的距离 | | 37 | ` dist = distancePoints3d(p1, p2, varargin)` | 两个点之间的距离 | | 38 | `[dist, proj] = distancePointTriangle3d(point, triangle)` | 点与三角形之间的最短距离 | | 39 | `drawAxis3d(varargin)` | 画一个彩色的坐标系和远点，图标 | | 40 | `varargout = drawEdge3d(varargin)` | 绘制边 | | 41 | `drawBox3d` | 绘制一个三维的立方盒子 | | 42 | `varargout = drawCircle3d(varargin)` | 绘制一个三维的圆 | | 43 | `varargout = drawCircleArc3d(arc, varargin)` | 绘制一个圆弧 | | 44 | `varargout = drawCube(cube, varargin)` | 绘制一个三维的立方体，最后旋转 | | 45 | `varargout = drawCuboid(cuboid, varargin)` | 绘制三维的长方体 | | 46 | `varargout = drawCylinder(cyl, varargin)`| | 47 | `varargout = drawEllipse3d(varargin)` | 绘制三维椭圆 | | 48 | `varargout = drawEllipseCylinder(cyl, varargin)` | | 49 | `varargout = drawEllipsoid(elli, varargin)` | 绘制椭球体 | | 50 | `varargout = drawGrid3d(varargin)` | 绘制3D网格 | | 51 | `varargout = drawLabels3d(varargin)` | 指定3D位置绘制标签 | | 52 | ` drawPlane3d(plane, varargin)` | 绘制被当前坐标系裁剪的平面| | 53 | ` varargout = drawPlatform(plane, siz, varargin)` | 画一个给定尺寸的矩形平台 | | 54 | `h = drawPoint3d(varargin)` | 绘制三维点 | | 55 | `varargout = drawPolygon3d(varargin)` |绘制由顶点坐标列表指定的三维多边形| | 56 | `varargout = drawPolyline3d(varargin)` | 绘制由顶点坐标列表指定的三维折线。 | | 57 | `varargout = drawSphere(varargin)` | 画一个球体的网格 | | 58 | `varargout = drawSphericalEdge(sphere, edge, varargin)` | 在球面上画一条边 | | 59 | ` varargout = drawSphericalPolygon(sphere, poly, varargin)` | 画一个球面多边形 | | 60 | `len = edgeLength3d(edge, varargin)`| 三维边的长度 | | 61 | `line = edgeToLine3d(edge)` |将三维边转换成线 | | 62 | ` s = ellipsoidSurfaceArea(elli)` | 球体的表面积 | | 63 | `ell = equivalentEllipsoid(points)` | 三维点集的等效椭球面 | | 64 | ` mat = eulerAnglesToRotation3d(phi, theta, psi, varargin)` | 将三维欧拉角转换为三维旋转矩阵 | | 65 | `varargout = fillPolygon3d(varargin)` | 填充由顶点坐标列表指定的3D多边形 | | 66 | `varargout = fillSphericalPolygon(sphere, poly, germ)` | 填充一个球面多边形 | | 67 | `varargout = fillSphericalTriangle(sphere, p1, p2, p3, varargin)` | 在球体上填充一个三角形 | | 68 | `trans = fitAffineTransform3d(pts1, pts2)` | 使用两个点集拟合仿射变换 | | 69 | `[fittedCircle, circleNormal] = fitCircle3d(pts)` | 拟合圆 | | 70 | `fitEllipse3d` | | 71 | `fitLine3d` | | 72 | `fitPlane` | | 73 | `h = hypot3(dx, dy, dz)` | 三维包围盒的对角线长度 | | 74 | `box = intersectBoxes3d(box1, box2)` | 三维盒子的交集| | 75 | `point = intersectEdgePlane(edge, plane, varargin)` | 边和面的交点| | 76 | `points = intersectLineCylinder(line, cylinder, varargin)` | 线和圆柱的交点 | | 77 | `point = intersectLinePlane(line, plane, varargin)` | 线和面的交点 | | 78 | `[inter, inside]= intersectLinePolygon3d(line, poly)` | 直线与三维多边形的交点 | | 79 | `points = intersectLineSphere(line, sphere, varargin)` | | 80 | `[point, pos, isInside] = intersectLineTriangle3d(line, triangle, varargin)` | 三维直线和三维三角形的交点 | | 81 | `line = intersectPlanes(plane1, plane2, varargin)` | 面和面的交线 | | 82 | `circle = intersectPlaneSphere(plane, sphere)` | 平面与球面的交点圆 | | 83 | `[inter, inside]= intersectRayPolygon3d(ray, poly)` | 三维射线与三维多边形的交点 | | 84 | `point = intersectThreePlanes(plane1, plane2, plane3)` | 三个面的交点 | | 85 | `below = isBelowPlane(point, varargin)` | 测试一个点在平面上还是平面下 | | 86 | `copl = isCoplanar(x,y,z,tol)` | 测试输入点的共面性 | | 87 | ` b = isParallel3d(v1, v2, varargin)` | 判断向量是否平行 | | 88 | `b = isPerpendicular3d(v1, v2, varargin)` | 判断向量的正交性 | | 89 | `d = isPlane(plane)` | 判断是否为面 | | 90 | `a = isTransform3d(trans, varargin)` | 判断是否为变换矩阵 | | 91 | `pos = linePosition3d(point, line)` | 返回投影在3D直线上的3D点的位置 | | 92 | `edge = lineToEdge3d(line)` | 将直线转化成边 | | 93 | `plane = medianPlane(p1, p2)` | 两点中间的平面 | | 94 | `box = mergeBoxes3d(box1, box2)` | 合并3D盒，通过计算他们的最大范围 | | 95 | `varargout = midPoint3d(varargin)` | 两个三维点的中点或三维边的中点 | | 96 | `plane2 = normalizePlane(plane1)` | 将平面的参数表示标准化 | | 97 | `vn = normalizeVector3d(v)` | 向量标准化 | | 98 | ` S = oblateSurfaceArea(elli, varargin)` | 近似扁椭球的表面积 | | 99 | `box3d = orientedBox3d(pts)` | 带朝向的包围盒 | | 100 | ` res = parallelLine3d(line, point)` | 创建平行的直线 | | 101 | ` res = parallelPlane(plane, point)` | 创建平行面 | | 102 | `n = planeNormal(plane)` | 计算平面的法向量 | | 103 | `coord = planePoint(plane, point)` | 计算平面上点的三维位置 | | 104 | `coord = planePoint(plane, point)` | 计算平面上点的三维位置-- | | 105 | ` pos = planePosition(point, plane)` | 计算点在平面上的位置-- | | 106 | `out = planesBisector(plane1, plane2)` | 两个其它平面之间的平分线平面 | | 107 | `theta = polygon3dNormalAngle(points, ind)` | 三维多边形顶点的法向角 |

``````% 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
%
%   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.
%   edges3d                     - Description of functions operating on 3D edges.
%   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.
%   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.
%   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.
%   clipLine3d                  - Clip a line with a box and return an edge.
%   drawEdge3d                  - Draw 3D edge in the current axes.
%   drawLine3d                  - Draw a 3D line clipped by the current axes.
%
% Planes
%   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.
%   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.
%   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.
%   intersectLinePolygon3d      - Intersection point of a 3D line and a 3D polygon.
%   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 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.
%
% 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.
%   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
%   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.
%
% Smooth surfaces
%   equivalentEllipsoid         - Equivalent ellipsoid of a set of 3D points.
%   fitEllipse3d                - Fit an ellipse to a set of points.
%   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.
%   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.
%
% 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        - Fit an affine transform using two 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.
%   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.
%
%
%   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@inra.fr
% Created: 2005-11-07
% Homepage: http://github.com/mattools/matGeom
% http://www.pfl-cepia.inra.fr/index.php?page=geom3d

% In development:
%   clipPolygon3dHP             - clip a 3D polygon with Half-space.
%   drawPartialPatch            - draw surface patch, with 2 parametrized surfaces.

% Deprecated:
%   vectorCross3d               - Vector cross product faster than inbuilt MATLAB cross.
%   inertiaEllipsoid            - Inertia ellipsoid of a set of 3D points.

% Others
``````
o

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