devDept.Geometry Moment of inertia and radii of gyration values. Moments of inertia about X coordinate axis. Moments of inertia about Y coordinate axis. Moments of inertia about Z coordinate axis. Radii of gyration about X coordinate axis. Radii of gyration about Y coordinate axis. Radii of gyration about Z coordinate axis. Base class for area and volume properties calculation. This method is called to obtain the results. Moments of Inertia about world coordinate axes This method is called to obtain the results. Second moment X Second moment Y Second moment Z Area Moments of Inertia about centroid coordinate axes Gets centroid. Area properties of a planar polygon or area properties of a solid defined by a triangle mesh. Empty constructor. Planar polygon constructor. Polygon plane Polygon vertices Accumulates additional segments. Polygon plane Polygon vertices Accumulate additional triangles. Vertices Triangles This method is called to obtain the results. Area Centroid First moment X First moment Y First moment Z Second moment X Second moment Y Second moment Z Product moment XY Product moment ZX Product moment YZ Moments of Inertia about world coordinate axes Area Moments of Inertia about centroid coordinate axes Gets area. Gets centroid. Volume properties of a solid defined by a triangle mesh. Empty construtor. Triangle list constructor. Vertices Triangles Accumulates additional triangles. Vertices Triangles This method is called to obtain the results. Mass Centroid First moment X First moment Y First moment Z Second moment X Second moment Y Second moment Z Product moment XY Product moment ZX Product moment YZ Moments of Inertia about world coordinate axes Area Moments of Inertia about centroid coordinate axes Gets solid mass. Gets solid centroid. Contains a collection of utility methods and constants. Planar fitting of 3D points using orthogonal regression. The set of points The plane. Linear fitting of 3D points using orthogonal regression. List of points to be fitted The line origin The line direction Least squares circle fit given a set of 2D points. List of 2D points to be fitted Plane of the 2D points The center of the circle The radius of the circle Least squares circle fit given a set of 3D points. List of 3D points to be fitted The plane of the circle, whose origin is the center of the circle The radius of the circle Returns the bounding rectangle of a collection of 2D points. A collection of 2D points. The min 2D point The max 2D point Returns the bounding rectangle of a collection of 2D points. A collection of 2D points. The min 2D point The max 2D point Returns the bounding box of a collection of 3D points. A collection of 3D points. The min 3D point The max 3D point Computes the bounding box of the given array of points. The transformation applied to the points The set of points The minimum point of the bounding box The maximum point of the bounding box Computes the bounding box of the given array of points. The transformation applied to the points The set of points Number of points The minimum point of the bounding box The maximum point of the bounding box Computes the bounding box of the given array of points. The set of points The minimum point of the bounding box The maximum point of the bounding box Computes the bounding box of the given array of points. The set of points Number of points The minimum point of the bounding box The maximum point of the bounding box Check if two bounding boxes overlap or touch. First rectangle min 2D point First rectangle max 2D point Second rectangle min 2D point Second rectangle max 2D point True if the two boxes overlap or touch, false otherwise. Check if two bounding rectangles overlap. First rectangle min 2D point First rectangle max 2D point Second rectangle min 2D point Second rectangle max 2D point The 2D domain size True if the two rectangle overlap or coincide, false otherwise. Check if two bounding rectangles overlap. First rectangle min point First rectangle max point Second rectangle min point Second rectangle max point True if the two rectangles overlap, false otherwise. Check if two bounding rectangles overlap. First rectangle min 2D point First rectangle max 2D point Second rectangle min 2D point Second rectangle max 2D point True if the two rectangles overlap, false otherwise. Check if two bounding boxes overlap. First rectangle min 3D point First rectangle max 3D point Second rectangle min 3D point Second rectangle max 3D point True if the two rectangles overlap, false otherwise. Check if two bounding boxes overlap or touch. First box min 3D point First box max 3D point Second box min 3D point Second box max 3D point True if the two boxes overlap or touch, false otherwise. Check if two bounding boxes overlap or touch. First box min 3D point First box max 3D point Second box min 3D point Second box max 3D point The domain size True if the two boxes overlap or touch, false otherwise. Check if two bounding boxes overlap or touch. First box min 3D point First box max 3D point Second box min 3D point Second box max 3D point The domain size True if the two boxes overlap or touch, false otherwise. Computes the intersection rectangle between two axis aligned rectangles. This function assumes that the two rectangles overlap. First rectangle min point First rectangle max point Second rectangle min point Second rectangle max point Intersection rectangle min point Intersection rectangle max point The size of the intersection rectangle Computes the intersection rectangle between two axis aligned boxes. This function assumes that the two boxes overlap. First box min point First box max point Second box min point Second box max point Intersection box min point Intersection box max point The size of the intersection box Tests if a 2D point is inside a 2D polygon. The test 2D point The polygon True if the 2D point is inside, false if the point is outside. For points on the edges of the polygon, please use The polygon must be closed, so the first and last points of the list must be coincident. Tests if a 2D point is inside a 2D polygon. The test 2D point The polygon The maximum diagonal size of the relevant polygon The point status. Tests if a 2D point is inside to a region composed by multiple 2D polygons (clockwise/anticlockwise orientation rule). The test 2D point The region as a collection of properly oriented 2D polygons The maximum diagonal size polygon The point status. Tests if a 2D point is inside to a region composed by multiple 2D polygons (clockwise/anticlockwise orientation rule). The test 2D point The region as a collection of properly oriented 2D polygons True if the point is inside the outer loop and outside all the inners loop, false otherwise. Tests if a 2D point is inside to a 2D rectangle. The test 2D point Rectangle lower left corner Rectangle upper right corner The point status. Point in triangle test. The point's X-coordinate The point's y-coordinate The first triangle vertex's X-coordinate The first triangle vertex's y-coordinate The second triangle vertex's X-coordinate The second triangle vertex's y-coordinate The third triangle vertex's X-coordinate The third triangle vertex's y-coordinate Returns true if the point is inside the triangle. Cleans a triangles list from the duplicated vertices. The triangles list The vertices list The triangles list without degenerate triangles The vertices list without the duplicated vertices Cleans the triangles from the duplicated vertices The triangles list The vertices list The triangles list without degenerate triangles The vertices list without the duplicated vertices the vertices conversion indices Compares two floating point numbers using the provided domain size. First floating point number Second floating point number The domain size True if the two numbers are equal, false otherwise. Converts radians to degrees. The angle in radians The converted angle in degrees. Converts degrees to radians. The angle in degrees The converted angle in radians. Clamps a value between the specified lower and upper limits. The type of the value to clamp Lower limit The value Upper limit Returns the min of three values. First value Second value Third value The maximum value. Returns the max of three values. First value Second value Third value The maximum value. Returns the next 'circular' node in the linked list. Current node The next 'circular' node. Returns the previous 'circular' node in the linked list. Current node The previous 'circular' node. Converts a float[4] to . Converts a to a float[4] with components in the [0,1] range. Converts Millimeters to Inches. The distance in Millimeters The distance in inches. Converts Inches to Millimeters. The distance in Inches The distance in Millimeters. Evaluates unit tangent and curvature from first and second derivatives. T = D1 / |D1| K = ( D2 - (D2 o T)*T )/( D1 o D1) First derivative Second derivative Unit tangent returned here Curvature returned here Reverses the order of the elements in the array. Items type The one-dimensional array to reverse Convert a list of double values to a 2D point array. An array of double values A list of 3D points. Converts an array of doubles to a an array of 3D points. An array of doubles The 3D point array. Converts an array of doubles to a an array of 4D points (only the XYZ members are converted). An array of doubles The 4D point array. Appends the second array at the end of first one. First rectangular array Second rectangular array A single array containing first and second. Inverts a matrix. The matrix to invert The inverted matrix True if successful, false otherwise. Gets the array of Point3D from a 2D profile. The sketch plane the 2D contour The Point3D array. Gets the first valid plane found from a collection of triangles. The collection of triangles The collection of vertices The first valid plane found. Computes the signed area of a polygon (the points are always projected on XY plane). The list of 2D points Depending on the polygon direction will return a positive or negative area. Computes the number of arc subdivisions according to specified chordal error. The arc radius The arc span angle (in radians) The chordal error The number of segments. Computes the number of circle subdivisions according to specified chordal error. The circle radius The chordal error The number of segments. Swaps two values. The type of values to swap First value Second value Returns the angle in degrees between two vectors. First Vector Second Vector Roation Axis The angle in degrees between the vectors Tells if a hypothetical sphere with the specified center and radius is inside the given frustum planes. Frustum planes Center of the sphere Radius of the sphere True if the hypothetical sphere is inside the planes. Useful for bounding box testing. Determines if a point in on a segment. First it checks if the parameter t for the projected point is between 0 and 1, then it checks if the test point is close enough to the segment. Gets a list of edges without duplicates from a mesh of triangles. Polygon list definition, each row can have indipendently 3 or 4 indices. Number of vertices in the mesh The rectangular array of the resulting - unique - edges. First and second indices are the edge vertex indices, third and fourth are the parent triangle indices. Fourth index can be -1 for edges with only one parent triangle. Gets a list of edges without duplicates from a mesh of polygons (3 or 4 sided mixed). Polygon list definition, each row can have indipendently 3 or 4 indices. Number of vertices in the mesh An array of linked list of - unique - edges propagating from the same vertex. This is an intermediate result. The rectangular array of the resulting - unique - edges. First and second indices are the edge vertex indices, third and fourth are the parent triangle indices. Fourth index can be -1 for edges with only one parent triangle. Gets a list of edges without duplicates from a mesh of triangles or quads. Polygon list definition, dimensions can be [n,3] or [n,4]. Number of vertices in the mesh The rectangular array of the resulting - unique - edges. First and second indices are the edge vertex indices, third and fourth are the parent triangle indices. Fourth index can be -1 for edges with only one parent triangle. Gets a list of edges without duplicates from a mesh of triangles or quads. Polygon list definition, dimensions can be [n,3] or [n,4]. Number of vertices in the mesh An array of linked list of - unique - edges propagating from the same vertex. This is an intermediate result. The rectangular array of the resulting - unique - edges. First and second indices are the edge vertex indices, third and fourth are the parent triangle indices. Fourth index can be -1 for edges with only one parent triangle. Gets a list of edges without duplicates from a mesh of triangles or quads. Polygon list definition, dimensions can be [n,3] or [n,4]. Number of vertices in the mesh An array of linked list of - unique - edges propagating from the same vertex. This is an intermediate result. The number of edges. Gets a list of faces without duplicates from a mesh of triangles or quads. Polygon list definition, dimensions can be [n,3] or [n,4]. Number of vertices in the mesh An array of linked list of - unique - faces propagating from the same vertex. This is an intermediate result. The rectangular array of the resulting - unique - faces. First, second and third indices are the face vertex indices, third and fourth are the parent objects indices. Fourth index can be -1 for faces with only one parent object. Intersects the infinite line with a plane. First point of the line Second point of the line The plane equation The intersection point (if exists) True if the intersection was found, false otherwise. Multiplies two matrices. first matrix second matrix The matrix a x b. Multiplies two matrices. first matrix second matrix The matrix a x b. Multiplies a matrix by a vector. The matrix The vector The vector "matrix x vect" Returns the outer loop index. The point type The list of 2D contours The outer loop index, -1 if the loops aren't nested. Returns the outer loop index. The point type The list of 2D contours The outer loop index Returns the outer contour index. The list of 2D contours The tolerance used to tessellate contours The outer loop index Removes contiguous duplicated points from the list. A point type The list of points to be analyzed The cleaned array of points. Removes contiguous duplicated points from the list. A point type The list of points to be analyzed The indices in the list of the returned points The cleaned array of points. Removes contiguous duplicated points from the list. A point type The list of points to be analyzed If true, computes also the indices of the final points The indices in the of the returned points The cleaned array of points. Gets the transformation to orient an entity built on the X-Axis on the given direction. The point where the entity must be positioned The orientation desired The transformation to orient the entity. Checks whether the triangle is inside or crossing the frustum defined by the given planes. The first triangle vertex The second triangle vertex The third triangle vertex The frustum planes equations True if the triangle is inside or is crossing the frustum. Tells if a segment is inside or crossing the given frustum. The camera frustum The segment True if the segment intersects or is inside the given camera frustum. Transforms the collection of normals with the given transformation. The transformation The collection of normals vectors The normals are transformed by the inverse transpose of the upper 3x3 matrix. Gets the matrix needed for normals transformation. The transformation The inverse transpose of the upper 3x3 matrix. Craetes a translation matrix and muliplies the original matrix by it. The X translation coefficient The Y translation coefficient The Z translation coefficient The matrix to multiply Craetes a scaling matrix and muliplies the original matrix by it. The X scaling coefficient The Y scaling coefficient The Z scaling coefficient The matrix to multiply Return the cyclic previous item in a list. The item type The list The item index The previous item or the last item of the list in the case that itemIndex is equal to zero. Return the cyclic next item in a list. The item type The list The item index The next item or the first item of the list in the case that itemIndex is equal to the list length less one. Returns the interpolated normal at the point p somewhere in the middle of the 3D segment defined by the points p1 and p2. The segment start point The segment start normal (unit length) The segment end point The segment end normal (unit length) The point The 3D normal vector. Returns the interpolated normal at the point p somewhere in the middle of the 3D rectangular face defined by the points p1, p2, p3 and p4. The face first corner point The face first corner normal (unit length) The face second corner point The face second corner (unit length) The face third corner point The face third corner (unit length) The face fourth corner point The face fourth corner (unit length) The point A 3D vector used for face splitting. A 3D vector perpendicular to the 3D face is not allowed. The 3D normal vector. Tells if a profile is closed, depending on a tolerance computed from its size. The type of the elements of the profile, must be derived from The list of vertices of the profile Computes a point on the Hermite Spline. Start point Start tangent End point End tangent Evaluation parameter The 2D point on the curve. Quad strip generation for Bar entity. Born for Bar entity, now used also for Fem Truss elements Tells if the point has valid coordinates for the OpenGL flaot precision. The point True if the point is within the OpenGL float precision, else otherwise. Detects polygon orientation (the points are always projected on XY plane). The polygon to check True if the polygon orientation is clockwise. Computes the signed area of a polygon (the points are always projected on XY plane). The list of points >0 for counterclockwise =0 for none (degenerate) lt;0 for clockwise. Rotates the array left. The array items type The array Returns the rotation axis and the angle to rotate from one vector to another. First vector Second vector The rotation axis The angle in degrees Checks if two generic lists contain the same elements. The first generic list The second generic list True if the elements of the two generic lists are the same. Traces two lines in 3D. x0(s) = p0 + s * t0 x1(t) = p1 + t * t1 Point on the first line First line direction Point on the second line Second line direction Value of s at the intersection Value of t at the intersection Intersection point, x0(s) = i = x1(t) See: http://hyperphysics.phy-astr.gsu.edu/hbase/ttrig.html The angle in radians Compares two objects. Matrix equation definition. Non zero values starting position. Non zero values ending position. List of elements with something to do with this dof. Is this dof restrained? Fixed displacement Coefficients. Matrix non zero term definition. Surface point definition. Curve point definition. Defines a 3D point. Defines a 2D point. Common properties of vertices. Gets the vertex position as a double array. Empty constructor. Standard constructor. Point's X coordinate Point's Y coordinate Double array constructor. Creates a deep copy of this 2D point. The new 2D point. Returns an array of point's coordinates. The double array. Returns true if the point's coordinates are resonable values. True if the point is valid, false otherwise. Addition between two 2D points. First 2D point Second 2D point The resulting 2D point. Subtraction between two 2D points. First 2D point Second 2D point The resulting 2D point. Product between a scalar value and a 2D point. Scalar value The 2D point The resulting 2D point. Product between a 2D point and a scalar value. Scalar value The 2D point The resulting 2D point. Division between a 2D point and a scalar value. Scalar value The 2D point The resulting 2D point. Project this point onto a 2D segment. The 2D segment The projected point. Computes the point-line distance. The line The distance between this 2D point and its projection on the line. Converts this 2D point to a human readable string. A string that represents this 2D point. Converts this 2D point to a human readable string. A string that represents this 2D point. Computes the distance between two 2D points. First point Second point The distance between a and b. Computes the squared distance between two 2D points. First point Second point The squared distance between p1 and p2. Computes the distance to 2D point b. The other point The distance between this 2D point and b. Compares two 2D points in the given domain. First point Second point The 2D diagonal length of your model. True if the two point are coincident, false otherwise. Calls glVertex2d(X, Y) Transforms the 2D point by the specified transformation. The transformation to be applied X coordinate value. Y coordinate value. Gets the absolute value of maximum coordinate. The absolute value of maximum coordinate. Returns a 2D point at origin. Returns a 2D point with coordinates at double.MinValue. Returns a 2D point with coordinates at double.MaxValue. Empty constructor. Standard constructor. X coordinate value Y coordinate value Z coordinate value 2D point constructor X coordinate value Y coordinate value Double array constructor. Creates a deep copy of this 3D point. The new 3D point. Returns an array of point's coordinates. The double array. Computes the distance to 3D point b. The other point The distance between this 3D point and b. Computes the distance between two 3D points. First 3D point Second 3D point The distance between a and b. Project this point onto a 3D segment. The 3D segment The projected point. Computes the point-line distance. The line The distance between this 3D point and its projection on the line. Computes the squared distance between two 3D points. First point Second point The squared distance between a and b. Computes the point-plane distance. The plane The distance between this 3D point and its projection on the plane. Subtraction between two 3D points. First 3D point Second 3D point The resulting 3D point. Product between a 3D point and a scalar s. Scalar value The point The resulting 3D point. Product between a 3D point and a scalar s. Scalar value The point The resulting 3D point. Division between a 3D point and a scalar s. Scalar value The point The resulting 3D point. Addition between a 3D point and a 3D vector. The 3D point The 3D vector The resulting 3D point. Subtraction between a 3D point and a 3D vector. The 3D point The 3D vector The resulting 3D point. Addition between two 3D points. First 3D point Second 3D point The resulting 3D point. Compares two 3D points in the given domain. First point Second point The 3D diagonal length of your model. True if the two point are coincident, false otherwise. Converts this 3D point to a human readable string. A string that represents this 3d point. Converts this 3D point to a human readable string. A string that represents this 2D point. Calls glVertex3d(X, Y, Z). Transforms the 3D point by the specified transformation. The transformation to be applied Z coordinate value. Returns the (0,0,0) point. Returns a 3D point with coordinates at double.MinValue. Returns a 3D point with coordinates at double.MaxValue. Parametric U value. Creates a deep copy of this 3D point. The new 3D point. Converts this 3D point to a human readable string. A string that represents this 3D point. Parametric V value Converts this 3D point to a human readable string. A string that represents this 3D point. 3D point and tangent definition. Tangent's X component. Tangent's Y component. Tangent's Z component Standard constructor. Creates a deep copy of this point. The new intersection point object. Gets or sets the 3D tangent associated to this 3D point. 3D point, tangent and U definition. Parametric U value Creates a deep copy of this point. The new intersection point object. Point cloud point definition. Surface's normal X component. Surface's normal Y component. Surface's normal Z component Shared edge definition. Other edge vertex index. Index of the first triangle that shares this edge. Index of the second triangle that shares this edge. Shared face definition. Other face second vertex index. Other face third vertex index. Other face fourth vertex index. Index of the first triangle that shares this edge. Index of the second triangle that shares this edge. Linear (length) unit system type. Inches Feet Miles Millimeters Centimeters Meters Kilometers Unit system not specified The unit system of the imported geometry is not supported by Eyeshot Angular unit system type. Degrees Radians 2D point with integer coordinates. Optionally can be linked to a . Defines an edge using vertex indices First vertex index. Second vertex index. Empty constructor Standard constructor Index of the line start vertex Index of the line end vertex Creates a deep copy of this index line. The new index line. Returns an array of line's vertex indices. The int array. Defines a triangle using vertex indices. Third verted index. Empty constructor. Standard constructor. Index of the first triangle vertex Index of the second triangle vertex Index of the third triangle vertex Creates a deep copy of this IndexTriangle. The new IndexTriangle. Returns an array of triangle's vertex indices. The int array. Computes the triangle quality. A collection of 2D points representing the 2D mesh vertices. The triangle quality (from 0 to 1) Interval definition. Left interval value. Right interval value. Standard constructor. Double array constructor. Swaps t0 and t1. Changes interval to [-t1, -t0]. Convert normalized parameter to interval value, or pair of values. Tests a value t to see if it is inside the interval. Value to test If false, t is tested to see if it satisfies min <= t <= max. If true, t is tested to see if it satisfies min < t < max. True if t is in the interval and false if t is not in the interval. Computes the union of the two intervals. First interval Second interval The resulting interval. Converts this Interval to a human readable string. A string that represents this Interval. Gets the left interval value. Gets the left interval value. Gets the right interval value. Gets the right interval value. Returns true if t0 > t1. Returns true if t0 < t1. Returns t1 - t0. Returns 0.5 * (t0 + t1). Returns smaller of t0 and t1. Returns larger of t0 and t1. Returns true if the interval length is 2*PI. Matrix operations helper class. Provides matrix multiplication, inversion and determinant computation methods. Returns true when the matrix is Identity. The matrix True when the matrix is Identity, false otherwise Scalar by matrix multiplication. The scalar value The matrix 3x3 matrix by scalar multiplication. The matrix The scalar value The multiplication result. 4x4 matrix by scalar multiplication. The matrix The scalar value The multiplication result. Matrix by scalar multiplication. The matrix The scalar value The multiplication result. 3x3 scalar by matrix multiplication. The scalar value The matrix The multiplication result. 4x4 matrix by matrix multiplication. The left matrix The right matrix The multiplication result. Matrix by matrix multiplication. The left matrix The right matrix The multiplication result. Matrix by matrix multiplication. The left matrix The right matrix The multiplication result. Computes the transpose of a matrix. The left matrix The transposed matrix. Computes the determinant of a 3x3 matrix. The matrix The matrix determinant. Computes the determinant of a 2x2 matrix. The matrix The matrix determinant. Computes the inverse of a 3x3 matrix. The matrix The inverse matrix True if the operation succeeded, false otherwise. Computes the determinant of a 4x4 matrix. The matrix The matrix determinant. Computes the inverse of a 4x4 matrix. The matrix The inverse matrix True if the operation succeeded, false otherwise. Plane intersection type. Disjoint (no intersection) The two planes coincide Intersection in a unique line Plane definition. XY plane constructor. 3D point and normal vector constructor. Point on the plane Non-zero normal to the plane Normal vector constructor. Non-zero normal to the plane 3D point, and two vectors constructor. Point on the plane Non-zero vector in plane Another vector in the plane not parallel to X Three non-colinear 3D points constructor. First point (Origin) Second point (X axis) Third plane (Y axis From equation constructor. Equation form: ax + by + cz + d = 0. Equation of plane Creates a deep copy of this plane. The new plane obejct. Creates the plane from three non collinear points. First point (Origin) Second point (X axis) Third point (Y axis) Updates plane equation. Reflects a point about this plane. Point to reflect The reflected point Reflects a point about this plane. Vector to reflect The reflected vector Evaluates a point on the plane. Point position Evaluates a point on the plane. Evaluation parameter Evaluation parameter Evaluates a point on the plane. Evaluation parameter Evaluation parameter Elevation parameter Computes the intersection of two planes. The first plane The second plane The intersection segment (when it exists) The intersection type. Computes the intersection of two planes. The first plane The second plane The intersection point (when it exists) The intersection direction The intersection type. Transforms the plane by the provided transformation. The transformation to be applied Returns a new plane with the specified offset from this one. The offset amount The new plane object. Rotates this plane around an axis passing through world origin. Rotation angle Rotation axis Rotates this plane. Rotation angle Rotation axis Origin point Translates this plane. Delta X Delta Y Delta Z Translates this plane. Delta vector Gets signed distance from the plane to a point. The distance Flip plane orientation by swapping X and y axes, reversing the zaxis, and updating the equation. Gets point on plane that is closest to a given point. The 3D point The s parameter of the closest point on the plane The t parameter of the closest point on the plane Gets point on plane that is closest to a given point. The 3D point The closest 2D point on the plane. Constructor for deserializing objects. A instance that defines the serialized data. A instance that contains the serialized data. Populates a instance with the data needed to serialize the target object. A instance that defines the serialized data. A instance that contains the serialized data. Converts this Plane to a human readable string. A string that represents this Plane. Gets the XY plane. Gets the YZ plane. Gets the ZX plane. Gets or sets the plane origin. Gets the plane X axis. Gets the plane Y axis. Gets the plane Z axis. Gets the plane equation. Plane equation definition. 3D Vector definition. Empty constructor. 2D constructor. Vector's X component Vector's Y component 3D constructor. Vector's X component Vector's Y component Vector's Z component Double array constructor. The array of doubles Two 3D points constructor. A 3D vector with direction from P0 to P1. First point Second point Three 3D points constructor. A 3D vector perpendicular to a plane defined by 3 points. Origin point Point along the X axis Point along the Y axis Check before using this 3D vector. Creates a deep copy of this 3D vector. The new 3D vector. Sets this vector to be perpendicular to another vector. The result is not normalized. The test 3D vector False if input vector is zero, true otherwise. Sets all the vector components to zero. Subtraction between two vectors. Addition between two 3D vectors. Addition between a 3D point and a 3D vector. Multiplication between a scalar value and a 3D vector. Multiplication between a 3D vector and a scalar s. Division between a 3D vector and a scalar s. Resizes the 3D vector to unit length. True if the operation succeeded, false otherwise. Dot product between two 3D vectors. Dot product between two 3D vectors. Dot product between a 3D vector and a 3D point. Dot product between a 3D point and a 3D vector. Subtraction between two 3D points. The first 3D point The second 3D point The resulting 3D vector. Addition between two 3D points. The first 3D point The second 3D point The resulting 3D vector. Cross product between two 3D vectors. The resulting 3D vector, not normalized. Cross product between two 3D points. The resulting 3D vector, not normalized. Computes the angle between two vectors. The angle in radians in the range 0 < angle < PI. First 3D vector (unit length) Second 3D vector (unit length) Converts this 3D vector to a human readable string. A string that represents this 3D vector. Reverses the 3D vector direction. Returns true if the angle between the two 3D vectors is zero. First 3D vector (unit length) Second 3D vector (unit length) Returns true if the angle between the two 3D vectors is zero or almost zero. First 3D vector (unit length) Second 3D vector (unit length) Dot product comparison tolerance Returns true if the angle between the two 3D vectors is PI. First 3D vector (unit length) Second 3D vector (unit length) Returns true if the angle between the two 3D vectors is PI or almost PI. First 3D vector (unit length) Second 3D vector (unit length) Dot product comparison tolerance Returns true if the angle between the two 3D vectors is 0 or PI. First 3D vector (unit length) Second 3D vector (unit length) Returns true if the angle between the two 3D vectors is zero or PI or almost zero or almost PI. First 3D vector (unit length) Second 3D vector (unit length) Dot product comparison tolerance Returns true if the angle between the two 3D vectors is PI/2. First 3D vector (unit length) Second 3D vector (unit length) Returns true if the angle between the two 3D vectors is PI/2 or almost PI/2. First 3D vector (unit length) Second 3D vector (unit length) Dot product comparison tolerance Calls glNormal3d(X, Y, Z) Transforms the 3D vector by the specified transformation. The transformation to be applied Returns the X axis vector. Returns the Y axis vector. Returns the the Z axis vector. True if the vector has length equal to zero. True if the vector has length equal to one. Gets or sets the 3D vector length. Gets or sets the vector length. Gets the angle between the X-axis and the vector projection on the XY plane. The angle in radians. Gets the angle between the vector and the XY plane. The angle in radians. D term. Empty constructor. 3D point and 3D normal constructor. 3D point on the plane 3D vector perpendicular to the plane Creates a plane equation from a 3D point and 3D normal vector. It sets (X,Y,Z) to a unitized N, then sets D = -(X*P.X + y*P.Y + Z*P.Z). 3D point on the plane 3D vector perpendicular to the plane True if the operation succeeded, false otherwise. Plane's coefficients constructor. Equation form: ax + by + cz + d = 0. First coefficient Second coefficient Third coefficient Fourth coefficient Creates a deep copy of this plane equation. The new plane equation object. Evaluate the plane at a point. The point x*P.x + y*P.y + z*P.z + d Evaluate the plane at a point. The x coordinate The y coordinate The z coordinate X*x + Y*y + Z*z + D Checks if this plane equation is valid. Converts this planar equation to a human readable string. A string that represents this planar equation. Returns an array of plane equation's coefficients. The double array. Defines a point in homogeneous coordinates. Empty constructor. 2D euclidean point constructor (Z=0, W=1). Point's X coordinate Point's Y coordinate 3D euclidean point constructor (W=1). Point's X coordinate Point's Y coordinate Point's Z coordinate Homogeneous point constructor. Point's X coordinate Point's Y coordinate Point's Z coordinate Point's W coordinate Double array constructor. 3D point constructor. The 3D point Creates a deep copy of this point. The new 4D point. Returns an array of point's coordinates. The double array. Product between a scalar value and a 4D point. Scalar value The 4D point The resulting 4D point. Division between a 4D point and a scalar s. Scalar value The 4D point The resulting 4D point. Addition between two 4D points. First 4D point Second 4D point The resulting 4D point. Subtraction between two 4D points. First 4D point Second 4D point The resulting 4D point. Computes the 4D distance. First 4D point Second 4D point The distance. The weights are treated as ordinary coordinates. Converts this 4D point to a human readable string. A string that represents this point. Transforms the homogeneous point by the specified transformation. The transformation to be applied W term. Gets or sets the Euclidean representation for this homogeneous point. Colored 3D point definition. Color constructor. Point's X coordinate Point's Y coordinate Point's Z coordinate Point's color Individual color components constructor. Point's X coordinate Point's Y coordinate Point's Z coordinate Point's color red component Point's color green component Point's color blue component Creates a deep copy of this RGB point. The new RBG point object. Red component. Green component. Blue component. Polygon status type. Over +--------------+ On | Clip +--+----+ | o-------+--o | | | In | | | | | +----+--+ | | | | +--+----+ | | | | | | +-------+ | | | | o----------o +--------------+ Out +---------+ | | +---------+ The subject polygon is inside the clip one The subject polygon is outside the clip one The subject polygon intersects the clip one The clip polygon is inside the subject one Point status type. Outside Inside Onto the polygon perimeter Closed 2D polygon definition. Polygon's bounding rectangle min point. Polygon's bounding rectangle max point Polygon's points. Points only constructor. The number of 2D points Points only constructor. The list of 2D points Points and bounding rectangle corners constructor. The list of 2D points The polygon's bounding rectangle min point The polygon's bounding rectangle max point Update/initialize the polygon min and max 2D points. Checks that Min and Max are not null/Nothing and that the polygon is closed. Checks if the provided 2D point is inside the 2D polygon bounding rectangle. The 2D point True if the 2D point is inside the bounding rectangle of the 2D polygon, false otherwise. Checks if the provided 2D point is inside or onto the 2D polygon bounding rectangle. The 2D point True if the 2D point is inside or onto the bounding rectangle of the 2D polygon, false otherwise. Checks if the provided 2D point is inside or onto the 2D polygon bounding rectangle. The 2D point The domain size True if the 2D point is inside or onto the bounding rectangle of the 2D polygon, false otherwise. Tests if a 2D point is inside the 2D polygon. The test 2D point True if the 2D point is inside, false otherwise. Tests if a 2D point is inside or onto the 2D polygon. The test 2D point The maximum size of the problem The point status. Check the status of the subject polygon against the clip one. Second polygon The 2D domain diagonal The subject polygon status. Gets Points.Count Defines a rotation in three dimensions. X term of this quaternion. Y term of this quaternion. Z term of this quaternion. W term of this quaternion. Quaternion components constructor. The X component of this quaternion The Y component of this quaternion The Z component of this quaternion The W component of this quaternion Axis and angle constructor. The rotation axis (normalized) The rotation angle in degrees Creates a new Quaternion from specified yaw, pitch, and roll angles. The yaw angle, in radians, around the y-axis. The pitch angle, in radians, around the x-axis. The roll angle, in radians, around the z-axis. Creates a deep copy of this quaternion. The new quaternion object. Resets this Quaternion to the rotation specified. The rotation axis (normalized) The rotation angle in degrees Gets current rotation. The rotation axis The rotation angle in degrees Gets current rotation. Rotation matrix Gets current inverse rotation. Inverse rotation matrix Used internally to rotate the camera because it must move in the opposite direction. Normalizes this Quaternion. True if the operation succeeded, false otherwise. Multiplies the specified quaternion by another. First quaternion Second quaternion The Quaternion that is the product of multiplication. Multiplies the specified quaternion by a scalar. Quaternion Scalar value The Quaternion that is the product of multiplication. Multiplies the specified quaternion by a scalar. Scalar value Quaternion The Quaternion that is the product of multiplication. Adds two quaternions. First quaternion Second quaternion The Quaternion resulted from the sum. Converts this Quaternion to a human readable string. A string that represents this Quaternion. Gets the identity Quaternion. Defines a 2D segment. Start point. End point. Empty constructor. Point2D constructor. Start point End point System.Drawing.Point constructor. Start point End point Individual coordinates constructor. The X value of start point The Y value of start point The X value of end point The Y value of end point Creates a deep copy of this 2D segment. The new 2D segment. Finds the point on the (infinite) line that is closest to given point. Test point The parameter of the point on the line that is closest to test point. Finds the point inside the segment that is closest to given point. Test point The parameter of the point on the line that is closest to test point. Evaluates a point on (infinite) segment. Evaluation parameter (1-t)*start + t*end Computes the intersection of two 2D segments. First segement Second segment Intersection point (when it exists) Endpoint of the intersect segment [i0, i1] (when it exists) The maximum diagonal size of the domain The intersection type. Computes the intersection of two infinite 2D lines. First line Second line Intersection point (when it exists) True if the intersection exists, false otherwise (parallel lines). Computes the intersection of two 2D segments. First line Second line Intersection point (when it exists) True if the intersection exists, false otherwise (parallel or disjoint). If return value is true and i0 is null, the segments are collinear and overlapping. Computes the intersection of two 2D segments. First line Second line Intersection point (when it exists) True if the intersection exists, false otherwise (parallel or disjoint). Here we return true even when the intersection is on the boundary of one of the two segments. Converts this 2D segment to a human readable string. A string that represents this 2D segment. Extends the segment of the amount provided. Extension amount at segment start Extension amount at segment end Returns true if the two segments are collinear. The first segment The second segment Gets the segment mid point. Gets the 2D segment length. Gets the 2D segment normal vector (not normalized). If true, the segment is a degenerated one (a point). 2D segment intersection type. Disjoint The two segments touch at end points (are contiguous) The intersection point is the end point of one of the segments Intersect in unique point i0 Overlap in segment from i0 to i1 The two segments touch at end points and are collinear Defines a 3D segment. Start point. End point. Empty constructor. Point3D constructor. Start point End point Individual coordinates constructor. The X value of start point The Y value of start point The Z value of start point The X value of end point The Y value of end point The Z value of end point Creates a deep copy of this 3D segment. The new 3D segment. Extends (if necessary) the segment to the provided 3D point. The extension point Finds the point on the (infinite) line that is closest to given point. Test point The parameter of the point on the line that is closest to test point. Finds the point inside the segment that is closest to given point. Test point The parameter of the point on the segment that is closest to test point. Evaluates a point on (infinite) segment. Evaluation parameter (1-t)*start + t*end Intersects a 3D segment with a plane. The plane The intersection point (if exists) True if the intersection was found, false otherwise. Intersects a 3D segment with a plane. The plane If true, the Segment3D is treated as an infinite line The intersection point (if exists) True if the intersection was found, false otherwise. Intersects the 3D segment with a plane. The plane equation True if the intersection was found, false otherwise. Intersects the 3D segment with a plane. The plane equation If true, the Segment3D is treated as an infinite line True if the intersection was found, false otherwise. Intersects the 3D segment with a plane. The plane equation The intersection point (if exists) True if the intersection was found, false otherwise. Intersects the 3D segment with a plane. The plane equation If true, the Segment3D is treated as an infinite line The intersection point (if exists) True if the intersection was found, false otherwise. Intersects the 3D segment with a triangle. First triangle vertex Second triangle vertex Third triangle vertex The intersection point (if exists) True if the intersection was found, false otherwise. Intersects the 3D segment with a triangle. First triangle vertex Second triangle vertex Third triangle vertex When true, it considers a ray starting from P0 to infinite The intersection point (if exists) The triangle s coordinate The triangle t coordinate True if the intersection was found, false otherwise. Converts this 3D segment to a human readable string. A string that represents this 3D segment. Returns true if the two segments are collinear. The first segment The second segment If true, the segment is a degenerated one (a point). Gets the 3D segment middle point. Gets the 3D segment length. Gets the 3D segment length squared. Defines a 2D size. Standard constructor. Two 2D points constructor. Returns the rectangle diagonal length. Gets the minimum rectangle dimension. Gets the maximum rectangle dimension. Defines a 3D size. Standard constructor. Two 3D points constructor. Gets the box diagonal length. Gets the minimum box dimension. Gets the maximum box dimension. 4x4 transformation matrix. Usage example. Transformation tra = new Transformation(); tra.Translation(10, 0, 0); Transformation rot = new Transformation(); rot.Rotation(Math.PI/6, Vector3D.AxisY); // angle in radians Transformation xform = tra * rot; // combines the two transformations (order matters) Point3D pt = new (10, 20, 30); Point3D newPt = xForm * p; // transforms the point pt Dim tra As Transformation = New Transformation() tra.Translation(10, 0, 0) Dim rot As Transformation = New Transformation() rot.Rotation(Math.PI/6, Vector3D.AxisY) ' angle In radians Dim xform As Transformation = tra * rot ' combines the two transformations (order matters) Dim pt As Point3D = New (10, 20, 30) Dim ptNew As Point3D = xForm * p ' transforms the point pt Zero matrix constructor. Diagonal matrix constructor. Diagonal value 4x4 square array of doubles constructor. The matrix (deeply copied) 16x array of doubles constructor. The matrix as an array of 16 doubles (deeply copied) ordered by row Check if the transformation is the 'Identity' one. 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 Test tolerance Returns true if matrix is the identity transformation. Check if the transformation is the 'Identity' one. 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 Returns true if matrix is the identity transformation. As frame constructor. 3D point X axis vector (unit length) Y axis vector (unit length) Z axis vector (unit length) Creates a deep copy of this transformation. The new transformation object. All zeros. Diagonal is (1,1,1,1). Diagonal 3x3 with bottom row = 0,0,0,1. Diagonal value Creates non-uniform scale transformation with the origin as a fixed point. Scale factor along X Scale factor along Y Scale factor along Z Creates non-uniform scale transformation with the origin as a fixed point. Scale vector Create uniform scale transformation with a specified fixed point. Fixed point Scale factor Create a non-uniform scale transformation with a specified fixed point. Fixed point Scale factor along X Scale factor along Y Scale factor along Z Right column is (dx, dy, dz, 1). Delta X Delta y Delta Z Right column is (v.X, v.Y, v.Z, 1). Delta vector Get transformation that projects to a plane. This transformation maps a 3D point P to the point plane.ClosestPointTo(Q). Plane to project to Applies transformation to a 2D point. The transformation The point The transformed point. Applies transformation to a 2D point. The transformation The vertex The transformed point. Applies transformation to a 3D point. The transformation The point The transformed point. Applies transformation to a RGB point. The transformation The point The transformed point. Applies transformation to a 4D point. The transformation The point The transformed point. Applies transformation to a 2D vector. The transformation The point The transformed vector. Applies transformation to a 3D vector. The transformation The point The transformed vector. Transposes the 4x4 matrix. Inverts the 4x4 matrix. True if matrix is non-singular, false otherwise. Rotation transformation. Angle in radians Rotation axis Rotation transformation. Angle in radians Axis start point Axis end point Rotation transformation. Angle in radians Rotation axis Center point Rotation transformation. StartPoint direction End direction Center point Rotation transformation. The frames should be right hand orthonormal frames (unit vectors with Z = X X Y). The resulting rotation fixes the origin (0,0,0), maps initial X to final X, initial Y to final Y, and initial Z to final Z. First frame X axis First frame Y axis First frame Z axis Second frame X axis Second frame Y axis Second frame Z axis Rotation transformation. The frames should be right hand orthonormal frames (unit vectors with Z = X X Y). The resulting rotation fixes the origin (0,0,0), maps initial X to final X, initial Y to final Y, and initial Z to final Z. If the initial and final center are equal, then that center point is the fixed point of the rotation. If the initial and final point differ, then the resulting transform is the composition of a rotation fixing P0 and translation from P0 to P1. The resulting transformation maps P0 to P1, P0+X0 to P1+X1, ... First frame Second frame Rotation transformation. The frames should be right hand orthonormal frames (unit vectors with Z = X X Y). The resulting rotation fixes the origin (0,0,0), maps initial X to final X, initial Y to final Y, and initial Z to final Z. If the initial and final center are equal, then that center point is the fixed point of the rotation. If the initial and final point differ, then the resulting transform is the composition of a rotation fixing P0 and translation from P0 to P1. The resulting transformation maps P0 to P1, P0+X0 to P1+X1, ... First frame Origin First frame X axis First frame Y axis First frame Z axis Second frame Origin Second frame X axis Second frame Y axis Second frame Z axis Mirror transformation. Mirror plane Mirror transformation. Point on mirror plane AxisZ of mirror plane Adds two transformations. Left one Right one The resulting transformation Subtract two transformations. Left one Right one The resulting transformation Computes a change of basis transformation. If you have points defined with respect to planes, the version of ChangeBasis() that takes two planes computes the transformation to change coordinates from one plane to another. The predefined world plane Plane.XY can be used as an argument. If P = plane0.Evaluate(a0, b0, c0) and (a1,b1,c1) = ChangeBasis(plane0, plane1) * new Point3D(a0, b0, c0) then P = plane1.Evaluate(a1, b1, c1) The version of ChangeBasis() that takes six vectors maps (a0, b0, c0) to (a1, b1, c1) where a0*X0 + b0*Y0 + c0*Z0 = a1*X1 + b1*Y1 + c1*Z1. The version of ChangeBasis() that takes six vectors with center points maps (a0, b0, c0) to (a1, b1, c1) where P0 + a0*X0 + b0*Y0 + c0*Z0 = P1 + a1*X1 + b1*Y1 + c1*Z1. The change of basis transformation is not the same as the rotation transformation that rotates one orthonormal frame to another. See the Rotation() method. True if the operation succeeded, false otherwise Initial plane Final plane Computes a change of basis transformation. Initial frame X (X,Y,Z = arbitrary basis) Initial frame Y Initial frame Z Final frame X (X,Y,Z = arbitrary basis) Final frame Y Final frame Z True if the operation succeeded, false otherwise Computes a change of basis transformation. Change of basis transformations and rotation transformations are often confused. This is a change of basis transformation. If Q = P0 + a0*X0 + b0*Y0 + c0*Z0 = P1 + a1*X1 + b1*Y1 + c1*Z1 then this transform will map the point (a0,b0,c0) to (a1,b1,c1) Initial frame center Initial frame X (X,Y,Z = arbitrary basis) Initial frame Y Initial frame Z Final frame center Final frame X (X,Y,Z = arbitrary basis) Final frame Y Final frame Z True if the operation succeeded, false otherwise. True if the scale factor of the transformation is the same in the X, Y and Z directions. Dumps the matrix on Console window. Constructor for deserializing objects. A instance that defines the serialized data. A instance that contains the serialized data. Populates a instance with the data needed to serialize the target object. A instance that defines the serialized data. A instance that contains the serialized data. Direct access on matrix values. Gets or sets the 4x4 matrix. Gets the 4x4 matrix as an array of doubles ordered by row. Gets the 4x4 matrix as an array of doubles ordered by column. Gets the scale factor along X. Gets the scale factor along Y. Gets the scale factor along Z. Identity transformation. Transformation Class Standard constructor. Constructor for deserializing objects. A instance that defines the serialized data. A instance that contains the serialized data. Translation transformation. Transformation Class Standard constructor. Delta X Delta y Delta Z 3D vector constructor. Delta vector Constructor for deserializing objects. A instance that defines the serialized data. A instance that contains the serialized data. Populates a instance with the data needed to serialize the target object. A instance that defines the serialized data. A instance that contains the serialized data. Rotation transformation. Angle and axis constructor. Angle in radians Rotation axis passign through origin Angle, axis and center point constructor. Angle in radians Rotation axis Center point Angle, axis start point and end point constructor. Angle in radians Axis start point Axis end point Constructor for deserializing objects. A instance that defines the serialized data. A instance that contains the serialized data. Populates a instance with the data needed to serialize the target object. A instance that defines the serialized data. A instance that contains the serialized data. Scale transformation. Uniform scale factor constructor. Scale factor Non-uniform scale factor constructor. Scale factor along X Scale factor along Y Scale factor along Z 3D vector constructor. Scale vector 3D point and scale factor constructor. Fixed point Scale factor 3D point and scale factors constructor. Fixed point Scale factor along X Scale factor along Y Scale factor along Z Constructor for deserializing objects. A instance that defines the serialized data. A instance that contains the serialized data. Populates a instance with the data needed to serialize the target object. A instance that defines the serialized data. A instance that contains the serialized data. Mirror transformation. Standard constructor. Mirror plane Constructor for deserializing objects. A instance that defines the serialized data. A instance that contains the serialized data. Populates a instance with the data needed to serialize the target object. A instance that defines the serialized data. A instance that contains the serialized data. Defines a 2D vector. Empty constructor. Standard constructor. Vector's X component Vector's Y component Two 2D points constructor. A 2D vector with direction from P0 to P1. First point Second point Double array constructor. The array of doubles Creates a deep copy of this 2D vector. The new 2D vector. Multiplication between a scalar value and a 2D vector. Scalar value The 2D vector Multiplication between a scalar value and a 2D vector. Scalar value The 2D vector Subtraction between two 2D points. The first 2D point The second 2D point The resulting 2D vector. Addition between two 2D points. The first 2D point The second 2D point The resulting 2D vector. Resizes the 2D vector to unit length. True if the operation succeeded, false otherwise. Inverts the 2D vector direction. Computes the angle between two 2D vectors. The angle in radians in the range 0 < angle < PI. First 2D vector (unit length) Second 2D vector (unit length) Computes the angle between two 2D vectors. The angle in radians in the range -PI < angle < +PI. First 2D vector Second 2D vector Perpendicular dot product. First 2D vector (unit length) Second 2D vector (unit length) The perpendicular dot product value. Subtraction between two 2D vectors. Addition between two vectors. Dot product between two 2D vectors. Dot product between two 2D vectors. Dot product between a 2D vector and a 2D point. Dot product between a 2D point and a 2D vector. Sets all the vector components to zero. Returns true if the angle between the two 2D vectors is zero. First 2D vector (unit length) Second 2D vector (unit length) Returns true if the angle between the two 2D vectors is zero or almost zero. First 2D vector (unit length) Second 2D vector (unit length) Dot product comparison tolerance Returns true if the angle between the two 2D vectors is PI. First 2D vector (unit length) Second 2D vector (unit length) Returns true if the angle between the two 2D vectors is PI or almost PI. First 2D vector (unit length) Second 2D vector (unit length) Dot product comparison tolerance Returns true if the angle between the two 2D vectors is 0 or PI. First 2D vector (unit length) Second 2D vector (unit length) Returns true if the angle between the two 2D vectors is zero or PI or almost zero or almost PI. First 2D vector (unit length) Second 2D vector (unit length) Dot product comparison tolerance Returns true if the angle between the two 2D vectors is PI/2. First 2D vector (unit length) Second 2D vector (unit length) Returns true if the angle between the two 2D vectors is PI/2 or almost PI/2. First 2D vector (unit length) Second 2D vector (unit length) Dot product comparison tolerance Converts this 2D vector to a human readable string. A string that represents this 2D vector. Reverses the 2D vector direction. Transforms the 2D vector by the specified transformation. The transformation to be applied True if the vector has length equal to one. True if the vector has length equal to zero. Gets or sets the 2D vector length. Gets the 2D vector squared length. Returns the X axis vector. Returns the Y axis vector. Gets the angle between the X-axis and the 2D vector. The angle in radians.