Timeline for Intersection of Cones in Three Space
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 29, 2013 at 14:10 | comment | added | rhlewis | Thanks Robert. In the applications I have in mind, there are two cameras or sensors, one at the origin and one at (b,0,0). The one at the origin is primary. The solution should describe directly what the intersection "looks like" from the point of view of the origin. Projecting the intersection to the xy plane or yz plane is not immediately helpful. I set up some polynomial equations in a reasonable coordinate system (though maybe not the best) and got the resultant. It has 4201 terms. | |
| Jan 28, 2013 at 19:21 | comment | added | Qfwfq | Probably I'm not understanding the question, but if we are over the reals why not use the polynomial $[(u_1 x_1 + u_2 x_2 + u_3 x_3)^2 - \alpha^2 (x_1^2 + x_2^2 + x_3^2)]^2+[(v_1 (x_1 - b) + v_2 x_2 + v_3 x_3)^2 - \beta^2 (x_1^2 + x_2^2 + x_3^2)]^2=0$, that describes the same zero set and has few terms? | |
| Jan 28, 2013 at 19:15 | history | answered | Robert Israel | CC BY-SA 3.0 |