# The GNU 3DLDF Hyperbolæ 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

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## Introduction

2005.11.09.
I've now added the data type hyperbola to the 3DLDF language. It corresponds to the type class Hyperbola in the C++ code.

The 3DLDF code for generating the following image is in hyprb_00.ldf. TeX code for the including it is in hyprb_00.txt.

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## Intersections

The 3DLDF code for generating the following image is in hyprb_01.ldf. TeX code for the including it is in hyprb_01.txt.

The intersection points of a hyperbola h and a path p, such that h and p are coplanar, and the slope of p is finite and non-null.

The 3DLDF code for generating the following image is in hyprb_02.ldf. TeX code for the including it is in hyprb_02.txt.

The intersection points of a hyperbola h and a path p, such that h and p are coplanar, and the slope of p is infinite.

The intersection points of a hyperbola h and paths q0 and q1, such that h and q0, and h and q1, are non-coplanar. Perspective projection.

path q0 intersects the hyperbola at point i0. path q1 intersects the plane of the hyperbola at point i1, but not the curve itself.

The 3DLDF code for generating the following image is in hyprb_04.ldf.

The intersection of a hyperbola and a plane. Perspective projection.

The 3DLDF code for generating the following image is in hyprb_05.ldf.

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`points` can be classified according to their position with respect to a `hyperbola` by using the `location` operator. The 3DLDF code for generating the following image is in hyprb_03.ldf.