Message: 14
Date: Sat, 6 Aug 2005 18:53:26 -0700
From: TJ Frame <[EMAIL PROTECTED]>
Subject: a few geometry questions...
To: How to use Revolution <use-revolution@lists.runrev.com>
Message-ID: <[EMAIL PROTECTED]>
Content-Type: text/plain; charset=ISO-8859-1
Hi everyone,
1) If I have the points A and B, how would I determine point C that lies
along the slope but is X units in length from the origin (which will always
be point A)
I can find the total distance between A and B or the midpoint using the
distance and midpoint formulas, but I'm not sure how to plug in a specific
distance value.
2) I also need to be able to find out where a circle of a given radius
whose orgin is at A intersects that imaginary line. Given that A will always
be the origin of the circle and I only want the single intersection heading
towards point B I wouldn't need to check for all possible solutions such as
non-intersection etc.
Any help would be greatly appreciated.. I'm an artist by trade and haven't
messed with geometry and algebra since high school!
- TJ
TJ,
This may be more than you want to know. The intersection point
between a line and a circle is a lengthy calculation. (Actually there
a two points of intersection. See the function on how to get them
both.)
I have copied the function below. You can check out the
functionality in the following stack. Run the following in the msg
box.
go stack url
"http://home.infostations.net/jhurley/LineCircleIntersection.rev";
The intersection function is:
function theIntersectionPt tCircleName, aPt,bPt
--This function determines the point of intersection
--between the circle names tCircle name
--and the two points aPt and bPt
put the width of grc tCircleName /2 into a
put theLineAngle(aPt,bPt) into ABangle
--put 180/pi*ABangle into tempV
put the loc of grc tCircleName into cPt
put theLineAngle(aPt,cPt) into ACangle
--put 180/pi*ACangle into tempC
put ABangle - ACangle into alpha
if alpha is 0 then add .0001 to alpha
put theDist(aPt,cPt) into b
--law of sines
put b*sin(alpha)/a into sinBeta
if abs(sinBeta) > 1 then
choose the browse tool
return ""
else
put asin(sinBeta) into beta
end if
--There are two points of intersection
--with the impact circle. Gamma defines one and
--the other is at pi - gamma.
--The one closest to point A is:
put pi - beta into beta--Omit this step if you want the more distant point
--Or get both and return both. Use the two points as needed.
put 180/pi*beta into tempBeta
put pi - alpha - beta into gamma
if gamma > pi/2 then put pi-alpha-beta into gamma
put 180/pi*gamma into tempGamma
--Law of sines again
put a*sin(gamma)/sin(alpha) into c
put c*cos(ABangle)into dABx--vx/v into dBx
put c*sin(ABangle) into dABy--vy/v into dBy
--Get end points of line from aPt to intersection point
put item 1 of aPt into x
put item 2 of aPt into y
put x+dABx,y+dABy into tInterectionPt
return tInterectionPt
end theIntersectionPt
Jim
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