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Paul Nicholls
Guest
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 Posted: Sun Nov 21, 2004 11:21 pm Post subject: Finding angle between 'vertical' line and line hitting edge |
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A C
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/r |
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(x,y) / |
----/ |
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O |
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B
Looking at my ascii art above,
is there a fast way of finding out the angle between the line B-C and
the line B-A that is hitting the side of the circle at (x,y) of radius r?
--
Cheers,
Paul.
"The plastic veneer of civilization is easily melted in the heat of the
momemt" - Paul Nicholls.
[email]paul_nicholls (AT) hotmail (DOT) NOSPAM.com[/email]
Remove ".NOSPAM" to reply.
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Paul Nicholls
Guest
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| Posted: Sun Nov 21, 2004 11:51 pm Post subject: Re: Finding angle between 'vertical' line and line hitting e |
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"Paul Nicholls" <paul_nicholls (AT) hotmail (DOT) NOSPAM.com> wrote
| Quote: | A C
|
____ |
/r |
|--. | |
(x,y) / |
----/ |
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O |
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B
Looking at my ascii art above,
is there a fast way of finding out the angle between the line B-C and
the line B-A that is hitting the side of the circle at (x,y) of radius r?
--
Cheers,
Paul.
|
Actually it would be better if I asked this:
Assuming line B-C as 0 degrees for O, lines on the left of B-C being +ve
degrees, and any lines on the right of B-C being -ve degrees...
is there a fast way of finding out the max and min angles of the 2 lines
extending from the origin B to 1 point on each side of the circle (upto a
max/min of +90/-90 degrees from the 0 degree line)?
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Nils Haeck
Guest
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| Posted: Mon Nov 22, 2004 3:59 am Post subject: Re: Finding angle between 'vertical' line and line hitting e |
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Hi Paul,
Let's define these:
Point D is center of circle (your x, y)
Point E is where the line AB touches the radius.
Point F is the point when you drop a line from D down and where it crosses
AB
Point G is the point going from F to the right until it hits BC
Since DE must be orthogonal to AB, you can say:
tan(ve) = |DE| / |DF| (1) or
tan(ve) = r / |DF| (2) since r = |DE|
Triangles BAC and BFG are congruent, so
| Quote: | BG| : |BC| = |GF| : |AC| or
BG| = (x /|AC|) * |BC| (3) (assuming x positive to left from C)
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You also know that
y + |DF| + |BG| = |BC| so (assuming y positive downwards from C)
| Quote: | DF| = |BC| - |BG| - y (4)
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Now use (3) in (4), then (4) in (2):
tan(ve) = r / ( |BC| - ((x /|AC|) * |BC|) - y) or
-1 r
ve = tan (---------------------------)
(1 - (x / |AC|)) * |BC| - y
That's about best you can do.. you'll need at least one inverse goniometric
function and the rest is basic geometry.
I didn't check for errors  I suggest you draw it out first and check
carefully.
Nils Haeck
www.simdesign.nl
"Paul Nicholls" <paul_nicholls (AT) hotmail (DOT) NOSPAM.com> wrote
| Quote: | "Paul Nicholls" <paul_nicholls (AT) hotmail (DOT) NOSPAM.com> wrote in message
news:41a12311 (AT) newsgroups (DOT) borland.com...
A C
|
____ |
/r |
|--. | |
(x,y) / |
----/ |
|
|
|
O |
|
|
|
B
Looking at my ascii art above,
is there a fast way of finding out the angle between the line B-C and
the line B-A that is hitting the side of the circle at (x,y) of radius
r?
--
Cheers,
Paul.
Actually it would be better if I asked this:
Assuming line B-C as 0 degrees for O, lines on the left of B-C being +ve
degrees, and any lines on the right of B-C being -ve degrees...
is there a fast way of finding out the max and min angles of the 2 lines
extending from the origin B to 1 point on each side of the circle (upto a
max/min of +90/-90 degrees from the 0 degree line)?
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Mr. X
Guest
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| Posted: Mon Nov 22, 2004 5:43 pm Post subject: Re: Finding angle between 'vertical' line and line hitting e |
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how about the old trigonometry book ?
Think Nils has already answered ...
Rgds
"Paul Nicholls" <paul_nicholls (AT) hotmail (DOT) NOSPAM.com> wrote
| Quote: | A C
|
____ |
/r |
|--. | |
(x,y) / |
----/ |
|
|
|
O |
|
|
|
B
Looking at my ascii art above,
is there a fast way of finding out the angle between the line B-C and
the line B-A that is hitting the side of the circle at (x,y) of radius r?
--
Cheers,
Paul.
"The plastic veneer of civilization is easily melted in the heat of the
momemt" - Paul Nicholls.
[email]paul_nicholls (AT) hotmail (DOT) NOSPAM.com[/email]
Remove ".NOSPAM" to reply.
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