Editing Talk:2509: Useful Geometry Formulas
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Unconvinced by the cone! The equation shown, is correct for an isosceles triangle with a half-ellipse on its base. But that shape has 'corners' where the sides meet that half-ellipse. In a 3D projected view of an actual cone, the sides will meet the base ellipse at a tangent, meaning that it is more than a half-ellipse. But I suppose it's close enough as an approximation...[[Special:Contributions/172.69.55.131|172.69.55.131]] 15:57, 1 September 2021 (UTC) | Unconvinced by the cone! The equation shown, is correct for an isosceles triangle with a half-ellipse on its base. But that shape has 'corners' where the sides meet that half-ellipse. In a 3D projected view of an actual cone, the sides will meet the base ellipse at a tangent, meaning that it is more than a half-ellipse. But I suppose it's close enough as an approximation...[[Special:Contributions/172.69.55.131|172.69.55.131]] 15:57, 1 September 2021 (UTC) | ||
: I verified your claim by imagining the surface of the cone as formed by a set of lines extending from the different points on the ellipse to a single fixed point at the tip. No matter where you put that tip point, the outermost lines seem tangent to the ellipse. Seems it works for both perspective and orthographic projections. Updated the explanation. Randall's formula is incorrect, especially for very short cone projections. [[User:Baffo32|Baffo32]] ([[User talk:Baffo32|talk]]) 22:46, 1 September 2021 (UTC) | : I verified your claim by imagining the surface of the cone as formed by a set of lines extending from the different points on the ellipse to a single fixed point at the tip. No matter where you put that tip point, the outermost lines seem tangent to the ellipse. Seems it works for both perspective and orthographic projections. Updated the explanation. Randall's formula is incorrect, especially for very short cone projections. [[User:Baffo32|Baffo32]] ([[User talk:Baffo32|talk]]) 22:46, 1 September 2021 (UTC) | ||
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; It's 3am (okay 5am) and I made it really long! | ; It's 3am (okay 5am) and I made it really long! |