Latus rectum for the non-mathematician

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around calculating the length of a chord (latus rectum) for an elliptical shape with off-center axes, specifically in the context of an animator seeking assistance with a mathematical problem related to the geometry of ellipses.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant describes their specific elliptical shape and requests help in developing an algorithm to calculate the length of a chord perpendicular to the major axis.
  • Another participant proposes a mathematical approach by suggesting equations for two ellipses joined at the minor axis and provides a formula for calculating the length based on the position along the major axis.
  • A third participant cautions that the shape may not necessarily be two ellipses, indicating that the length of the chord could vary depending on the specific egg-shaped function used.
  • This participant also references a resource that lists various egg-shaped functions, implying that the problem may have multiple valid approaches depending on the chosen model.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the shape in question, with some suggesting it is two ellipses while others indicate that it could be a different type of egg-shaped function. The discussion remains unresolved regarding the best approach to calculate the chord length.

Contextual Notes

The discussion highlights potential limitations in the assumptions made about the shape and the mathematical models applicable, as well as the dependency on specific definitions of the egg-shaped functions.

bhnh
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I'm hoping someone can help me with this question. I'm an animator; the last math course I took was 40 years ago:bugeye:.

I have an elliptical shape wherein the major and minor axes intersect off-center, so I've got an egg shape (major axis=165, minor axis =80, intersection at 100,40). I have a line perpendicular to the major axis which can be positioned at any point along the major axis. What I need is a basic algorithm to figure the length of the resulting chord (latus rectum?).

I wouldn't want to admit to being desperate, but I am, kind of. Any help would be immensely appreciated.

Thanks!
 

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I suppose your shape is two ellipses joined at the minor axis. So you can write an equation for each one, with the origin at the intersection of the axes:

Left side:
x2/652 + y2/402 = 1

Right side:
x2/1002 + y2/402 = 1

The length is just 2*y. So rearrange for y:
If the line is on the left side:
length = 2 * sqrt( 402(1-x2/652) )
Where x is the distance from the intersection of the axes.
 
Out of sight. Thanks!:biggrin:
 

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