On 2010-10-17 03:05, Le_Forgeron wrote:
> Le 17/10/2010 07:38, Tim Cook nous fit lire :
>> I have a spline which I which to simplify to a series of CSGed cylinders
>> and boxes.
>>
>> cylinder 1 is located at 0, 0 with major and minor axes of 2 and 1.4375
>> cylinder 2 is located at 0.5, 2.875 with maj./min. axes of 1.786, 1.03125
>>
> Orientation ?

0 rotation, major axis along x.

> Are they true ellipses or just scaled circles ?

Er?  I thought that's what ellipses were...rather, a circle being a 
special case of an ellipse.  (One site I looked at mentioned scaling 
everything so one ellipse is a unit circle at origin and solving from 
there...?)

>> How do I find the endpoints of the tangent ascending from the left of
>> the lower circle to the right of the upper circle?
>
> Why do you need such endpoints ? (with precision)
> Wouldn't an approximation be enough ?

Well, enough precision to get a smooth surface in a render. 
Approximation is fine.  I'm working at five decimal places right now...

> Between 2 non colliding circles, there is 4 tangents. (two are crossings
> between the centers, the two others are parallel or crossing on the side
> of the smaller circle past its center)
> (well, symetry rules along the axis defined by the centers)

...which is why I (well, tried to) specify the particular one of those 
in which I'm interested.

>> (Also on this spline is needed a tangent descending from the left of the
>> lower circle to intersect point -2.03125, 0.21875, the method of
>> solution of which is probably related to the other problem)
>>
> The second case is just identical, a point is a 0-radius circle.

Figured as much.  I vaguely remember asking a similar question about two 
/circles/ on this or another group, but two ellipses is...a bit 
trickier.  Even just being able to figure out the slope of a tangent to 
a particular point on an ellipse would be a help.

-- 
Tim Cook

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