# Curve on surface with a constant inclination

Hello,
I need to create the orange curve on that surface with a constant inclination. Or in Grasshopper or in Rhino,
thanks for helping,
Roy

if the outer-surface is a cylinder
_helix
or
_shortPath
if the surface is not a cylinder, post the file please.

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UnrollSrfUV the curved wall.

Create the curve/line on the unrolled wall. The constant inclination curve will be a straight line on the rolled surface.

FlowAlongSrf the curve/line using the unrolled surface as the base and the curved wall surface as the target. FlowAlongSrf | Rhino 3-D modeling

Added: Or if the curved wall is part of circular cylinder use Helix as Tom suggested.

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interpolatecrvonsrf

Perhaps projecting a line would work as well.

ShortPath will provide a constant inclination curve if the surface is cylindrical.

Not if a constant inclination along the curve is desired; the geometry wonâ€™t work that way.

I prefer CurveOnSurface CurveOnSurface | Food4Rhino The V6 version also works in V7.

as i do skitours, this problem is fantastic - it is asking for the best uphill path - that will provide most comfortable walking.

So i am asking for the more general approach - what if the surface is freeform ?

if a startpoint and a slope / inclination is given - it s quite easy to incrementally build a curve approximation:

but if start and endpoint is given it s getting quite hard.
maybe a nice challenge to solve with kangaroo ?

I had been drew a lots of steel construction stairs.
You can use the â€śInterpCrvâ€ť to draw a curve form edges of stairs pedal .
You will get the curve and â€śpullâ€ť the curve to closest surface, and â€śunrollsrfâ€ť from inside surface to outside.

if u can post the file will be better.

Assuming you want a constant inclination then my guess is except for special cases such as cylindrical surfaces iteration is needed.

Thank you, Guys!
Lots of suggestions.
To Me:
Helix: Iâ€™m not able to create the curve with the given start and endpointâ€¦( )
Short path: It works here but it seems a little bit less precise than other methods (I mean very subtle difference in the resulting curve);
Unroll/FLow: It works perfectly;
Interpolatecrvonsrf: it works perfectly and is beautiful in that it shows the preview of the curve on surface while Iâ€™m drawing it - Itâ€™s my favourite method;
Projecting a line give differents result if the cylinder is not perfectly aligned to the view;
So, to me, Interpolate Crv is the better solution.

Jaw, I donâ€™t understand â€śYou will get the curve and â€śpullâ€ť the curve to closest surface, and â€śunrollsrfâ€ť from inside surface to outsideâ€ťâ€¦
Thanks all,
Roy

Helix

1. messure the angle of the base-Arc of the cylinder - fastest method i think:
_dupEdge or draw a new _arc
_what command will show the angle (example 95.8495) (copy)

make sure to messure the angle with one (better two) digits more, than your document-tolerance. you may need to increase the display precision in the _documentProperties
2. _helix the axis is the same as the cylinder has (cyan in my example)
3. mode = turn
4. input turn as a formula (95.8495/360) (i had to use paste in an external text editor and pasted the formular)
5. klick startpoint, optional correct the sign (+/-) of the turn
6. control the result _gcon against the edge is easy - should be G0.
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A really â€śscientificâ€ť solution, but the other methods are easierâ€¦anyway I will never arrive at this solution by myselfâ€¦

Hereâ€™s a thread on solving this type of problem iteratively.

Essentially itâ€™s keeping a list of points each at constant distance from the next, and with the same height increase, then pulling them onto the surface.
Itâ€™s quite fun for making zig-zagging mountain paths

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The curve on the surface is not constant inclination. The inclination increases as the diameter reduced.

@davidcockey : I might donâ€™t understan what youâ€™re looking for, but for me it doesnâ€™t seem to change the inclination:

yep, Iâ€™ve measured like a nooB

I assume â€śinclinationâ€ť means â€śslopeâ€ť (vertical distance gained for horizontal distance traveled), not vertical distance gained per revolution. For a road, ramp or steps it is usually desirable to keep the vertical distance gained for horizontal distance traveled constant or close to constant.

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you are climbing the same height with shorter and shorter lengths, of course, the inclination increasesâ€¦

ah,alright, translation issue, Iâ€™m sorry to have bothered you and thank you for the explanation!