Rhino Question about Control Points and Degrees

[CET]

Are there rules or guidelines for how many degrees to use relative to the number of control points when rebuilding a curve or surface? I know the fewer the control points, the more fair the curve or surface is likely to be, but the number of degrees is something I don’t understand. Any help appreciated!

[pavel915]

degree of curvature of curve is n+1, where n is the number of maximum and minimum point( chrest and trough) it have.
If the curve represensts a polynomial; degre is the highest power of "x" it have. As example if the equation of curve is x^3+x^2+2x+6=0 then the degree of the curve is said to be 3.

[zeroname]

for better understand, draw a simple curve , choose different degree and click preview , try it several time.. u can easily understand whats going on..


and pavel just say exactly that is written in the help file... so read help file to know more.. its simple

thanks

[Martijn_vE]

Usually a degree of 3 is enough for a fair surface. A higher degree is possible and often yield in smoother looking surfaces. On the other hand the area of influence of a control point is larger. This can be seen very well while drawing a curve. If you have a curve of degree 3 and move one of the control points the part of the curve that actually changes maximally has the length of 4 controlpoints, two on either side of the point you are moving. If you use a curve of degree 5 this length increases to 3 points on either side. This is the area of influence of a control point.

While modeling surfaces the same occurs, only this time in two directions. The larger this area of influence becomes the harder it gets to fair it.

[CET]

Usually a degree of 3 is enough for a fair surface. A higher degree is possible and often yield in smoother looking surfaces. On the other hand the area of influence of a control point is larger. This can be seen very well while drawing a curve. If you have a curve of degree 3 and move one of the control points the part of the curve that actually changes maximally has the length of 4 controlpoints, two on either side of the point you are moving. If you use a curve of degree 5 this length increases to 3 points on either side. This is the area of influence of a control point.

While modeling surfaces the same occurs, only this time in two directions. The larger this area of influence becomes the harder it gets to fair it.

Your explanation makes perfect sense. THANK YOU!!! :)