geometry: perpendicular segment and orthocenter corrections #1332
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The perpendicular segment may not terminate on the LinearEntity so the intersection must be done with the line containing the linear entity. The same sort of reasoning applies to the orthocenter calculation: since the altitudes are segments, they may not intersect within the triangle so lines containing the altitudes should be used to find the intersection.
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| perpendicular to the opposite side. | ||
| An altitude of a triangle is a segment through a vertex, | ||
| perpendicular to the opposite side, with length being the | ||
| height of the vertex measured from the line containing the side. |
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The original formulation is in correspondence with what Wikipedia says and with my rememberings from geometry. Is there a specific reason you wish to transition to a different definition?
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The original formulation misuses the word "line" (i.e. infinite line).
A "segment" is the part of the line between two points.
The wikipedia article uses the terms "line" and "segment" correctly,
however the meaning of "altitude" changes from "line" to "segment"
throughout the text.
This method returns the "altitude segment" so I think that the new
docstring is better.
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On Wed, Jun 6, 2012 at 4:51 PM, Stefan Krastanov
reply@reply.github.com
wrote:
@@ -1824,8 +1824,9 @@ def is_right(self):
def altitudes(self):
"""The altitudes of the triangle.
- An altitude of a triangle is a straight line through a vertex and
- perpendicular to the opposite side.
- An altitude of a triangle is a segment through a vertex,
- perpendicular to the opposite side, with length being the
- height of the vertex measured from the line containing the side.
The original formulation misuses the word "line" (i.e. infinite line).
A "segment" is the part of the line between two points.The wikipedia article uses the terms "line" and "segment" correctly,
however the meaning of "altitude" changes from "line" to "segment"
throughout the text.This method returns the "altitude segment" so I think that the new
docstring is better.
Yes, I was trying to make the docstring reflect what the function is
doing, and I agree with Stefan's observation about the wikipedia
article.
Does this read better?
An altitude of a triangle is a segment that is perpendicular to the
line containing a given side of the triangle and passing through the
vertex opposite that side.
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Oh, I haven't read the Wikipedia article to the end, so I didn't know there was abuse of terminology :-( The reason why I commented on this new definition was that, at first sight, it seemed rather unintuitive; I thought I had a better definition in mind, however, when I tried to actually put it down, it turned out to be very convoluted :-(
As for the new version of the definition, I like the first one better ("An altitude of a triangle is a segment through a vertex,..."). The first definition describes one end of the segment, orientation, and length, thus being complete. The second definition describes orientation and one point on the segment, which doesn't look sufficiently unambiguous to me. It is slightly more readable, but I rather wouldn't vote for it.
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OK, I'll commit what's there, then. Thanks for the attention in looking this over. |
geometry: perpendicular segment and orthocenter corrections
The perpendicular segment may not terminate on the LinearEntity so
the intersection must be done with the line containing the linear
entity. The same sort of reasoning applies to the orthocenter calculation:
since the altitudes are segments, they may not intersect within the triangle
so lines containing the altitudes should be used to find the intersection.
This addresses issue 3279.