The GNU 3DLDF Hyperbolæ Page

Author: Laurence D. Finston.

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Copyright (C) 2005, 2006 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

Table of Contents

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.

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.

Classifying Points with Respect to a Hyperbola

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.