drawing arc

[mdsalman2003]

This questions is more related to math than autocad. But someone might be able to give some help.

As we know in Autocad we can define an arc by using 3 points method. Now if I have a set of 3 points how can I check if I feed these points to the arc command arc will be drawn i.e. how to find that the points really define an arc. Certainly we can check it by running the arc command but I want some algorithm for check if the points are valid for drawing an arc.

Thanks.

[rkmcswain]

Can't an ARC be constructed through ANY 3 points, so long as they do not all lie on the same line?

[scott.wilcox]

Indeed, as long as the points are not in a line, an arc can be drawn.

[cadtag]

well, if the arc radius is infinite, then three points in a straight line would also fall on that arc. The center point would be the endpoint of the RAY drawn perpendiular from the midpoint (not a practical response, but logical. like much of math

[Coolmo]

well, if the arc radius is infinite, then three points in a straight line would also fall on that arc. The center point would be the endpoint of the RAY drawn perpendiular from the midpoint (not a practical response, but logical. like much of math

Is that even right? seems to me that the bigger the radius gets,.... the bigger... the radius gets. Since an ARC can be considered a piece of a circle and if you simply increase the radius of a circle FOREVER and an infinite amount of times, you'll simply get a bigger circle. If that's the case, wouldn't the ARC just keep growing in size and never reach a point of being straight?... which would be a finite 'thing" and therefore not infinite? To reach the stage of "straight" would suggest you can go past that and now your radius is negative... right? My head hurts.


Just asking....

[BeKirra]

This questions is more related to math than autocad. But someone might be able to give some help.

As we know in Autocad we can define an arc by using 3 points method. Now if I have a set of 3 points how can I check if I feed these points to the arc command arc will be drawn i.e. how to find that the points really define an arc. Certainly we can check it by running the arc command but I want some algorithm for check if the points are valid for drawing an arc.

Thanks.

It would be simple if you are working in WCS (2d).
In WCS all you have to do is
1) comparing the Z value for 3 points if they are 0.
2) check the angle between point1-point2 & point2-point3 if it is not equal to 180deg.

In a user defined UCS (3d) it would be a little bit different.
You have to work in that UCS defined by the 3 points first, then repeat the same process above.
Hope it helps.

[rkmcswain]

It would be simple if you are working in WCS (2d).
In WCS all you have to do is
1) comparing the Z value for 3 points if they are 0.
2) check the angle between point1-point2 & point2-point3 if it is not equal to 180deg.


In a user defined UCS (3d) it would be a little bit different.
You have to work in that UCS defined by the 3 points first, then repeat the same process above.
Hope it helps.

Very good point. My initial reply assumed that all three points were on the same plane.

EDIT:
In WCS - The three points do not have to all be at elevation 0, only at the same elevation.

[irneb]

...2) check the angle between point1-point2 & point2-point3 if it is not equal to 180deg....

Make that 180deg or 0deg.

Refer to attached: Geometrically you would be able to find the centre point of the arc by calculating the intersection of 2 lines (in red) drawn perpendicular between each pair of the 3 points (green) at the mid point of that distance (yellow). Then the radius of the circle (cyan) is the distance from that intersection to any of the points (blue).

As stated before: Of course with the 3d space you'll need some method of adjusting the pane to that of the 3 points as well.

How to prove this algebraically is beyond me at present ... I last did Calculus at varsity ... and that's a while back

[BeKirra]

Very good point. My initial reply assumed that all three points were on the same plane.

EDIT:
In WCS - The three points do not have to all be at elevation 0, only at the same elevation.

By default, in WCS any points drawn are with Z=0 unless the operator specified.
When the operator find any points with Z /= 0 in WCS, these points can be identified as not valid - actually these points are in a UCS (user defined) mathematically.
And this will help mdsalman2003 to find out the points which are "valid", I guess.

BTW, personally I usually don't talk about plane instead of WCS or UCS in AutoCAD as it is invisible - unlike the one in Inventor.

[BeKirra]

...
How to prove this algebraically is beyond me at present ... I last did Calculus at varsity ... and that's a while back

Well, you can prove it by a little lisp code - and which is beyond me, really.
You are a big one making LISP code, rkmcswain is the one as well.