=> 👽 sdfgeoff

Anyone here know how to parameterize equations - I'm a bit rusty.

Story: I want to create a mesh representation of a 2d distance field. The distance field is a low-resolution floating point grid and data is interpolated with bilinear interpolation. As far as I can tell, the easiest way to find points on the bounday is to rearrange the bilinear patch into parametric form: F(x,y) = value could turn into F(t) = (x,y) where (x,y) is a point where value = 0.

Some scribbling/eyeballing suggests the solutions are all conic sections?

3 years ago

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3 Replies

=> 👽 mc

I fail to completely understand whaich is your doubt, but I'll presume that what's on this link may help you: https://colalg.math.csusb.edu/~devel/precalcdemo/param/src/param.html · 3 years ago

=> https://colalg.math.csusb.edu/~devel/precalcdemo/param/src/param.html

=> 👽 sdfgeoff

For reference: F(x,y) = Axy + Bx(1-y) + C(1-x)y + D(1-x)(1-y)

Find solve for (x,y) where F(x,y) = 0

I'm not only interested in the solution, but also how it was achieved. · 3 years ago

=> 👽 sdfgeoff

The longer story is that I want to be able to detect line-intersection (raycast) against the zero-isoline of the low-resolution-floating-point-grid. I would raymarch, but bilinear surfaces can be highly non-linear so cannot be treated as a signed distance field. · 3 years ago