# The GNU 3DLDF Ellipsoids Page

Author: Laurence D. Finston.

This copyright notice applies to the text and source code of this web site, and the graphics that appear on it. The software described in this text has its own copyright notice and license, which can be found in the distribution itself.

Copyright (C) 2005, 2006, 2007 The Free Software Foundation

Permission is granted to copy, distribute, and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, with no Front-Cover Texts, and with no Back-Cover Texts. A copy of this license is included in the file COPYING.TXT

Last updated: April 29, 2006

Back to main page

## Introduction

2005.10.31.
I've now added the data type ellipsoid to the 3DLDF language. It corresponds to the type class Ellipsoid in the C++ code.

Ellipsoid

Back to contents
Back to main page

## Related Cuboids

2005.12.07.
I've now added parser rules and functions for finding the enclosing cuboid of an ellipsoid, i.e., the smallest cuboid that contains the ellipsoid. Finding the inscribed cuboid of an ellipsoid, i.e., the largest cuboid that fits into an ellipsoid, is more difficult. I don't yet know how to do this.

The 3DLDF code for generating the following four images is in elpsd_02.ldf.

Perspective Projection

Parallel Projection, X-Z Plane

Parallel Projection, X-Y Plane

Parallel Projection, Z-Y Plane

Back to contents
Back to main page

## Classifying Points with Respect to an Ellipsoid

`points` can be classified according to their position with respect to a `ellipsoid` by using the `location` operator:

```ellipsoid E;
set E with_center origin with_axis_x 24 with_axis_y 16 with_axis_z 10
with_divisions_x 8 with_divisions_y 8 with_divisions_z 2
with_point_count 64;
point p[];
p0 := (1, 2, 1);  %% Inside.
p1 := (4, 9, 0);  %% Outside.

ellipse e;
e := get_ellipse 3 E;

p2 := get_point 60 e; %% On the surface.

message "p0 location E:";
show p0 location E;

message "p1 location E:";
show p1 location E;

message "p2 location E:";
show p2 location E;
```

`location` returns one of the following numerical values:

 0: The `point` lies on the surface of the `ellipsoid`. 1: The `point` lies within the `ellipsoid`. -1: The `point` lies outside the `ellipsoid`. `INVALID_NUMERIC`: An error occurred.

In the following image, p0 lies inside the `ellipsoid`, p1 outside it, and p2 on its surface. The complete 3DLDF code for generating this image can be found in elpsd_06.ldf.

Back to contents
Back to main page

## Intersections

### The Intersection Points of an Ellipsoid and a Linear Path

2005.12.09.
The following four images illustrate the intersections of an `Ellipsoid` and a linear `Path`. The 3DLDF code for generating these images is in elpsd_13.ldf.

Back to contents
Back to main page

### The Intersection Points of an Ellipsoid and a Plane

2005.12.15.
The routine for finding the ellipse that represents the intersection of an ellipsoid and a plane.

The 3DLDF code for generating the following four images is in elpsd_17.ldf.

Perspective Projection

Parallel Projection, X-Z Plane

Parallel Projection, X-Y Plane

Parallel Projection, Z-Y Plane

Back to contents