Conic Evaluation of Line

Hi guys,

I am trying to create a definition which allows me transition between evaluating a line/curve linearly or progressively by a conic function.

On my try, I simply replicated the behavior of the graph mapper.

Sadly, the maximum I could achieve with this technique leaves a big space (hatched). (17.3 KB)

I found this thread where @DavidRutten shared a way of creating this conic curve, but I don’t think it is working properly: According to David,

if you set the middle slider to 0, you get a line.

But I still get a curve, never a line, and it also seems to be “jumping” from one curve to another.

Try using cubic bezier curve. Having the control (not end) points moving along the x and y axis while the end points are as shown above (minx, miny) and (maxx, maxy)

To be more exact, control point at the start will move along X axis. Control point at the end will move along (maxx, 0.0) - (maxx,maxy) axis

Hi Ivelin, thank you. I am not sure I am fully following you though, care to show an example? Thanks.

The conic in the Graph Mapper uses a three point nurbs curve. One control point at (0,0) one at (1,0) and one at (1,1)*. The only thing changing is the weight of the middle control point. If zero, you get a straight line, when approaching infinity, you get an L shape.

The only tricky bit is figuring out which exact weight yields an intersection between the conic and a custom point.

* for conics with their bulge pointing downwards only, the other case is just mirrored.

Hi Ivelin, thank you. I understand now.

I think my actual definition achieves the same result using “Nurbs Curve” component instead of the actual equations.

What I am trying to resolve is the inability of the curve to create an almost L shape, as with the graph mapper.

Try setting your slider to go to 100 0r 1000

Hi David, I am not controlling the weight, just the parameter, same as Ivelin. So the slider goes from 0.0 to 1.0.

I would use David’s technique, which uses weights, but it does not seem to be very consistent…

Edit: I just figured it out, the slider does not have to reach exactly 0 to generate a line.

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is this good enough? (11.4 KB)