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README
GeometRi
Simple and lightweight computational geometry library for .Net
This version is obsolete. Please use C# version of the library: GeometRi.CSharp
GeomtRi is a simple and lightweight 3D geometry library for .Net. It is not one more 3D graphics library, its main job is manipulations with basic geometrical primitives, such as point, line, plane, segment in 3D space: translation and rotation operations, distance calculation, intersections, orthogonal projections of one object into another, etc. The objects can be defined in global or in one of the local coordinate systems and converted form one coordinate system into another.
The library was build to be as simple and intuitive as posible. Users do not have to remember the reference coordinate system of each object. The objects store the coordinate system they are defined in and all transformations will be caried out implicitly when necessary.
The main goal was simplisity and readability of the code, therefore speed and robustness was not a priority. Global tolerance property is used for proximity checking, not an exact robust algorithms.
Installation
Use NuGet to install library. Search for GeometRi in NuGet package manager or type in the Package Manager Console:
InstallPackage GeometRi
Classes
Point3d and Vector3d are two base classes, representing points and vectors in 3D space. Objects of type Point3d or Vector3d can be defined in global or in local coordinate systems.
Line3d, Ray3d, Segment3d, Plane3d, Circle3d, Sphere, Ellipse and Triangle are compound classes, which are defined in terms of points and vectors.
Coord3d and Matrix3d are auxiliary classes.
GeometRi3d is an abstract class, which defines some common functionality, for example global tolerance property (GeometRi3d.Tolerance) used in proximity operations by other classes. Implements tolerance based equality methods: AlmostEqual(double, double), NotEqual(double,double), Greater(double, double) and Smaller(double, double).
Point3d
One of the base classes, can be constructed by three double numbers (X, Y and Z) or from double array. Each constructor has optional parameter 'coord' for local coordinate system in which point will be defined. By default all points are defined in global coordinate system.
Properties
 X  X coordinate in reference coordinate system
 Y  Y coordinate in reference coordinate system
 Z  Z coordinate in reference coordinate system
 Coord  reference coordinate system
 ToVector  radius vector of point ### Methods
 Clone  deep copy of object
 ConvertTo  convert point to local coordinate system
 ConvertToGlobal  convert point to global coordinate system
 Add  add two points
 Subtract  subtract one point from other
 Scale  scale point by given number
 DistanceTo  shortest distance from point to point, line, plane, ray or segment
 ProjectionTo  orthogonal projection of point to line, plane or sphere
 BelongsTo  check if point belongs to line, ray, segment, plane, circle, ellipse or sphere surface
 IsInside  check if point is inside circle or sphere
 Translate  translate point by vector
 Rotate  rotate point around origin or other point
 Reflect  reflect point in point, line or plane
 Equals  check if two points are equals
 ToString  string representation of point in global or local coordinate system ### Static methods
 CollinearPoints  check if three points are collinear ### Overloaded operators
 +  add two points
   subtract one point from other
   unary operator
 *  scale point by number
 /  scale point by number
 =  equality check
 <>  unequality check
Vector3d
Second base class, representing vector in 3D space. Constructed by three components (X, Y and Z) or from double array (with optional 'coord' parameter for local cordinate system). Additionally, can be constructed by point, representing radius vector of that point, or by two points, representing vector from first point to another. In this cases the vector will be defined in the same coordinate system as the first operand.
Properties
 X  X component in reference coordinate system
 Y  Y component in reference coordinate system
 Z  Z component in reference coordinate system
 Coord  reference coordinate system
 Norm  Norm of a vector
 ToPoint  point, represented by vector starting in origin
 OrthogonalVector  return arbitrary vector, orthogonal to the current vector ### Methods
 Clone  deep copy of object
 ConvertTo  convert vector to local coordinate system
 ConvertToGlobal  convert vector to global coordinate system
 Normalize  normalize the current vector
 Normalized  return normalized vector
 IsParallelTo  check if two vectors are parallel
 IsNotParallelTo  check if two vectors are NOT parallel
 IsOrthogonalTo  check if two vectors are orthogonal
 Add  overloaded, add number or vector
 Subtract  oveloaded, subtract number or vector
 Mult  overloaded, multiply by number or vector
 Dot  dot product of two vectors
 AngleTo  angle between vector and other vector, line, plane, ray or segment
 AngleToDeg  angle between vector and other vector, line, plane, ray or segment (in degrees)
 ProjectionTo  return projection of the current vector to the second vector
 Rotate  rotate vector around origin
 Reflect  reflect vector in point, line or plane
 Equals  check if two vectors are equals
 ToString  string representation of vector in global or local coordinate system
Line3d
Represent infinite line in 3D space and is defined by any point lying on the line and a direction vector.
Properties
 Point  base point of the line
 Direction  direction vector of the line ### Methods
 Clone  deep copy of object
 DistanceTo  shortest distance to point, line, ray or segment
 PerpendicularTo  point on the perpendicular to the second line
 IntersectionWith  intersection of line with plane or sphere
 ProjectionTo  orthogonal projection of a line to the plane
 AngleTo  angle between line and other line or plane
 AngleToDeg  angle between line and other line or plane (in degrees)
 Translate  translate line by vector
 Rotate  rotate line around origin or other point
 Reflect  reflect line in point, line or plane
 Equals  check if two lines are equals
 ToString  string representation of line in global or local coordinate system
Ray3d
Represent ray in 3D space and is defined by starting point and direction vector.
Properties
 Point  base point of the ray
 Direction  direction vector of the ray
 ToLine  convert ray to line ### Methods
 Clone  deep copy of object
 DistanceTo  shortest distance to point, line, segment or other ray
 PerpendicularTo  point on the perpendicular to the line
 IntersectionWith  intersection of ray with plane
 ProjectionTo  orthogonal projection of ray to the plane
 AngleTo  angle between ray and plane
 AngleToDeg  angle between ray and plane (in degrees)
 Translate  translate ray by vector
 Rotate  rotate ray around origin or other point
 Reflect  reflect ray in point, line or plane
 Equals  check if two rays are equals
 ToString  string representation of ray in global or local coordinate system
Segment3d
Represent a line segment in 3D space and is defined by two points.
Properties
 P1  first point of the segment
 P2  second point of the segment
 Length  length of the segment
 ToVector  convert segment to vector
 ToRay  convert segment to ray
 ToLine  convert segment to line ### Methods
 Clone  deep copy of object
 DistanceTo  shortest distance to point, line, ray, plane or other segment
 IntersectionWith  intersection of segment with plane
 ProjectionTo  orthogonal projection of segment to the line or plane
 AngleTo  angle between segment and plane
 AngleToDeg  angle between segment and plane (in degrees)
 Translate  translate segment by vector
 Rotate  rotate segment around origin or other point
 Reflect  reflect segment in point, line or plane
 Equals  check if two segments are equals
 ToString  string representation of serment in global or local coordinate system
Plane3d
Defined by arbutrary point on the plane and a normal vector. Optionally can be defined by coefficients in general equation of plane (Ax + By + Cz + D = 0), by three points or by point and two vectors in the plane.
Properties
 Point  point on the plane
 Normal  normal vector of the plane
 A/B/C/D  coefficients A, B, C and D in the general plane equation ### Methods
 Clone  deep copy of object
 SetCoord  set reference coordinate system for general plane equation
 IntersectionWith  intersection of plane with line, plane, sphere, circle or two other planes
 AngleTo  angle between plane and vector, line or plane
 AngleToDeg  angle between plane and vector, line or plane (in degrees)
 Translate  translate plane by vector
 Rotate  rotate plane around origin or other point
 Reflect  reflect plane in point, line or plane
 Equals  check if two planes are equals
 ToString  string representation of plane in global or local coordinate system
Sphere
Defines a sphere in 3D space. Implements intersection with line, plane and other sphere, projection to line and plane, as well as common translation, rotation and reflection methods.
Properties
 Center  center of the sphere
 R  radius of the sphere
 Area  area of the sphere
 Volume  volume of the sphere ### Methods
 Clone  deep copy of object
 DistanceTo  shortest distance to point, line, ray, segment or plane
 IntersectionWith  intersection of sphere with line, plane or other sphere
 ProjectionTo  orthogonal projection of sphere to the line or plane
 Translate  translate sphere by vector
 Rotate  rotate sphere around origin or other point
 Reflect  reflect sphere in point, line or plane
 Equals  check if two spheres are equals
 ToString  string representation of sphere in global or local coordinate system
Circle3d
Defines a circle in 3D space. Implements common translation, rotation and reflection methods.
Properties
 Center  center of the circle
 R  radius of the circle
 Normal  normal of the circle
 Perimeter  perimeter of the circle
 Area  area of the circle
 ToEllipse  convert circle to equivalent ellipse ### Methods
 Clone  deep copy of object
 ParametricForm  return point on circle for given parameter 't'
 ProjectionTo  orthogonal projection of circle to plane
 IntersectionWith  intersection of circle with plane
 Translate  translate circle by vector
 Rotate  rotate circle around origin or other point
 Reflect  reflect circle in point, line or plane
 Equals  check if two circles are equals
 ToString  string representation of circle in global or local coordinate system
Ellipse
Defines an ellipse in 3D space, represented by center point and two vectors, for major and minor semiaxes.
Properties
 Center  center of the ellipse
 MajorSemiaxis  major semiaxis of the ellipse
 MinorSemiaxis  minor semiaxis of the ellipse
 Normal  normal of the ellipse
 A  length of major semiaxis
 B  length of minor semiaxis
 F  distance from center to focus
 F1  first focus
 F2  second focus
 e  eccentricity of the ellipse
 Perimeter  approximate circumference of the ellipse
 Area  area of the ellipse ### Methods
 Clone  deep copy of object
 ParametricForm  return point on ellipse for given parameter 't'
 ProjectionTo  orthogonal projection of ellipse to plane
 Translate  translate ellipse by vector
 Rotate  rotate ellipse around origin or other point
 Reflect  reflect ellipse in point, line or plane
 Equals  check if two ellipses are equals
 ToString  string representation of ellipse in global or local coordinate system
Triangle
Defines a triangle n 3D space. Implements common translation, rotation and reflection methods. Calculates most of the standard triangle properties: bisectors, meadians, altitudes, incenter, circumcenter, centroid, orthocenter, etc.
Properties
 A/B/C  vertices of the triangle
 AB/AC/BC  length of the triangles' sides
 Perimeter  perimeter of the triangle
 Area  area of the triangle
 Circumcircle  circumcircle of the triangle
 Angle_A/B/C  angle at the vertex A/B/C
 Bisector_A/B/C  angle bisector at the vertex A/B/C
 Incenter  incenter of the triangle
 Centroid  centroid of the triangle
 Orthocenter  orthocenter of the triangle
 Circumcenter  circumcenter of the triangle
 Incircle  incircle of the triangle
 Altitude_A/B/C  altitude at the vertex A/B/C
 Median_A/B/C  median at the vertex A/B/C
 IsEquilateral  check if all sides of the triangle are the same length
 IsIsosceles  check if two sides of the triangle are the same length
 IsScalene  check if all sides are unequal
 IsRight  check if one angle is equal 90 degrees
 IsObtuse  check if one angle is greater than 90 degrees
 IsAcute  check if all angles are less than 90 degrees ### Methods
 Clone  deep copy of object
 Translate  translate triangle by vector
 Rotate  rotate triangle around origin or other point
 Reflect  reflect triangle in point, line or plane
 Equals  check if two triangles are equals
 ToString  string representation of triangle in global or local coordinate system
Coord3d
Class representing orthogonal cartesian 3D coordinate system. Defined by an origin point and transformation matrix (three orthogonal unit vectors stored in row format). One global coordinate system (Coord3d.GlobalCS) is defined by default, any number of local coordinate systems can be defined by users.
Properties
 Origin  origin of the coordinate system
 Axes  unit vectors of the axes, stored as rowmatrix(3x3)
 Name  name of the coordinate system
 Counts  total number of defined coordinate systems
 X/Y/Zaxis  X/Y/Zaxis of the coordinate system
 XY/XZ/YZ_plane  planes of the coordinate system ### Methods
 Clone  deep copy of object
 Rotate/RotateDeg  rotate coordinate system around rotation axis
 Equals  check if two coordinate systems are equals
 ToString  string representation of coordinate system
Matrix3d
Properties
 Item(i,j)  element of the matrix
 Row1/2/3  rows of the matrix
 Column1/2/3  columns of the matrix
 Det  determinant of the matrix
 MaxNorm  Max norm of the matrix
 IsZero  check if matrix is zero matrix
 IsIdentity  check if matrix is identity matrix
 IsOrthogonal  check if matrix is orthogonal ### Methods
 Inverse  inverse of the matrix
 Transpose  transpose of the matrix
 RotationMatrix  rotation around given axis
 Equals  check if two matrix are equals
 ToString  string representation of matrix
GeometRi3D
Properties
 Tolerance  tolerance used for comparison operations (default 1e12) ### Methods
 AlmostEqual  tolerance based equality check
 NotEqual  tolerance based unequality check
 Greater  tolerance based comparison
 Smaller  tolerance based comparison