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#Actualunbird

Posted 25 August 2013 - 05:18 AM

I just had an alternative idea using rasterization (if I understand your problem right, and you can project everything to a rectangular area):

- use a rendertarget, one channel, maybe even float precision, as big as you can/wish
- project your circles with simple alpha blending. You could even anti-alias the border
- do a manual mip-map downscale to compute the sum (parallel reduction)

Anyway: You got some screenshots/sketches for illustration ?

Hope that helps.

Edit: There's also the analytic way. The Area of Intersecting Ellipses (Eberly): Not sure if this covers "tilted" ellipses. This one does. Though I wonder if this is feasible/applicable if you have more than two ellipses overlapping.

#3unbird

Posted 25 August 2013 - 05:17 AM

I just had an alternative idea using rasterization (if I understand your problem right, and you can project everything to a rectangular area):

- use a rendertarget, one channel, maybe even float precision, as big as you can/wish
- project your circles with simple alpha blending. You could even anti-alias the border
- do a manual mip-map downscale to compute the sum (parallel reduction)

Anyway: You got some screenshots/sketches for illustration ?

Hope that helps.

Edit: There's also the analytic way. The Area of Intersecting Ellipses - Geometric Tools: Not sure if this covers "tilted" ellipses. This one does. Though I wonder if this is feasible/applicable if you have more than two ellipses overlapping.

#2unbird

Posted 25 August 2013 - 05:17 AM

I just had an alternative idea using rasterization (if I understand your problem right, and you can project everything to a rectangular area):

- use a rendertarget, one channel, maybe even float precision, as big as you can/wish
- project your circles with simple alpha blending. You could even anti-alias the border
- do a manual mip-map downscale to compute the sum (parallel reduction)

Anyway: You got some screenshots/sketches for illustration ?

Hope that helps.

Edit: There's also the analytic way. The Area of Intersecting Ellipses - Geometric Tools: Not sure if this covers "tilted" ellipses. [url="http://works.bepress.com/gbhughes/17/"]This one does. Though I wonder if this is feasible/applicable if you have more than two ellipses overlapping.

#1unbird

Posted 25 August 2013 - 05:07 AM

I just had an alternative idea using rasterization (if I understand your problem right, and you can project everything to a rectangular area):

- use a rendertarget, one channel, maybe even float precision, as big as you can/wish
- project your circles with simple alpha blending. You could even anti-alias the border
- do a manual mip-map downscale to compute the sum (parallel reduction)

Anyway: You got some screenshots/sketches for illustration ?

Hope that helps.

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