User Manual 3.4.1 Geometry : Différence entre versions

Version du 2 mars 2018 à 16:15

Introduction

Scope

The geometry objects implemented in the PATRIUS library are both infinite and finite shapes.

The finite shapes shall be used for example to represent parts of a spacecraft or celestial bodies. The infinite ones can represent more mathematical surfaces such as instruments' characteristics.

All the objects provide methods to compute interactions with lines (intersections, distances, etc...), points and other objects.

Javadoc

The geometry objects are available in the package org.commons.math3.geometry.euclidean.threed in the Commons Math Library (and Commons Math add-ons).

Links

Commons Math contains several other packages related to geometry (1D, 2D, 3D) and provides objects for Binary Space Partitioning (BSP) Tree. See javadoc for more information. Some other "basic" objects are contained in the Commons Math threed package and documented in other parts of this manual (eg : Rotations, Matrix3D).

Useful Documents

Useful reference documents for this theme can be found here :

• Nürnberg, R.; Distance from a Point to an Ellipse, Imperial College London, 2006, http://www2.imperial.ac.uk/~~rn/distance2ellipse.pdf.

Package Overview

The aim of the following diagram is to present the architecture implemented for the Geometry package. This does not mean that all the classes and/or interfaces are in the Geometry package and it doesnt mean that all the classes and interfaces of the package are presented.

Features Description

2D Objects

The two dimensional objects (in three dimensional space) implemented in the PATRIUS library are given hereunder :

• Lines
• Planes
• Plates
• Disks
• Ellipses

Please refer to the Classes section for more information.

3D Objects

The three dimensional objects (in three dimensional space) implemented in the PATRIUS library are given hereunder :

• Infinite and Finite Cylinders (right circular, elliptic and rectangular)
• Infinite and Finite Cones (right circular, oblique circular and rectangular)
• Spheres, Spheroids and Spherical Caps
• Parallelepipeds

Please refer to the Classes section for more information.

Interactions between objects

Interfaces have been implemented for geometrical objects in order to set a standard as to what method each and any geometrical object should implement.

As of now, (some of the) geometrical objects must provide methods to :

• Check if a line intersects with said objects,
• Compute and return the intersection points,
• Compute and return the closest point on the object surface to a given user point,
• Compute and return the distance between these two points,
• Compute and return the closest point on the object surface to a given user line and return the closest points on the line and on the object,
• Compute and return the distance between an object and a given user line.

Plese refer to the Interactions section for more details.

Getting Started

Interactions

Given an object implementing the Shape interface, the following methods are available :

intersects(Line) : boolean Test the intersection of the object with a user given line.

Code snippet :

Line line = new Line(lineOrigin, lineDirection);
boolean result = myObject.intersects(line);

getIntersectionPoints(Line) : Vector3D[] Compute the intersection point of the object with a user given line.

Code snippet :

Line line = new Line(lineOrigin, lineDirection);
Vector3D[] intersectionPoints = myObject.getIntersectionPoints(line);

closestPointTo(Vector3D) : Vector3D Compute the point on the surface of the object that is the closest to a user given point.

Code snippet :

Vector3D point = new Vector3D(1.0, 2.0, 3.0);
Vector3D result = myObject.closestPointTo(point);

distanceTo(Vector3D) : double Compute the shortest distance from the surface of the object and user given point.

Code snippet :

Line line = new Line(lineOrigin, lineDirection);
double distance = myObject.distanceTo(line);

closestPointTo(Line) : Vector3D[] Compute the points realizing the shortest distance to a line (the first one is from the line, the second one from the object ). If the line intersects the object , the two points are identical, and equal to the first one returned by the "getIntersectionPoints" method. If the line is parallel to the object 's side, the closest point to the origin is used.

Code snippet :

Line line = new Line(lineOrigin, lineDirection);
Vector3D[] points = myObject.closestPointTo(line);

distanceTo(Line) : double Compute the shortest distance from a line to the surface of the object.

Code snippet :

Line line = new Line(lineOrigin, lineDirection);
double distance = myObject.distanceTo(line);

Contents

Interfaces

Classes

Basic Shapes

Cylinders

NB : For the rectangular cylinder, please refer to the parallelepiped class mentioned above.

Cones

Ellipsoids

Other objects