Scott Rossi <[EMAIL PROTECTED]> wrote:
> Subject: Math Challenge
> Date: Thu, 08 Mar 2001 03:31:50 -0800
<snip>
> I'm wondering if someone good at geometric math might be able to figure out
> the following: how to drag an object relative to the points of a
> non-vertical ellipse (an oval which is rotated by some odd measurement).
An interesting diversion. Below are two handlers: drawE, mouseDown. Make
a new stack (default size OK) and put these into stack script, removing any
line breaks added by email program. Run draw E. Then click and drag your
mouse. Y direction pointing down kept, so angles run CW from positive x
axis. Scripts not optimized or double-checked, and seems to be an error in
exact location of "dot".
Rich Herz <ucsd.edu>
on drawE
global theta, a, b, yO, xO
# positive y and yp directions point down on screen
# so positive angle is rotation CW, rather than standard CCW when y
direction is up
# ellipse dimensions a & b are defined with respect to xp, yp axes
# xp, yp axes are rotated theta degrees from screen x,y axis
# ADJUSTABLE PARAMETERS:
put 30 into theta # (<= 90) angle xp,yp axis is rotated from x,y axis
put 50 into a # intersection of ellipse with xp axis
put 30 into b # intersection of ellipse with yp axis
put 150 into yO # y Offset of ellipse origin from window y zero
put 150 into xO # x Offset of ellipse origin from window x zero
put pi*theta/180 into thetaRad # thetaRad in radians
repeat with phi = 1 to 360 # phi in degrees
put pi*phi/180 into phiRad # phiRad in radians
put a*cos(phiRad) into xp
put b*sin(phiRad) into yp
# convert xp, yp of rotated ellipse coordinates into x,y screen coord.
put cos(thetaRad)*(xp - yp*cos(thetaRad)) into x
put yp/cos(thetaRad) + tan(thetaRad)*x into y
add xO to x
add yO to y
put round(x), round(y) into line phi of thePoints
end repeat
if there is not a graphic "ellipse" then
create graphic "ellipse"
set the style of graphic "ellipse" to "polygon"
end if
if there is not a graphic "dot" then
create graphic "dot"
set the style of graphic "dot" to "oval"
set the width of graphic "dot" to 10
set the height of graphic "dot" to 10
end if
set the points of graphic "ellipse" to thePoints
set the loc of graphic "dot" to xO, yO
end drawE
# ---------------------
on mouseDown
global theta, a, b, yO, xO
repeat while the mouse is down
put the mouseLoc into xy
put item 1 of xy into x
put item 2 of xy into y
subtract xO from x
subtract yO from y
if x = 0 then add 1 to x # to prevent divide by zero in atan(y/x) below
put atan(y/x) into sumThetaPhi # sumThetaPhi in radians
put sumThetaPhi*180/pi into sumThetaPhi # sumThetaPhi in degrees
# sumThetaPhi now ranges between +/- 90 degrees from nearest x axis
# convert to 0-360 range from positive x axis starting in positive y
direction (down, so CW here)
# first get quadrant, then handle separately for each quadrant (here,
positive y is down)
# xxx this may be too complex, just what worked first! xxx
# get quadrant
if x < 0 and y < 0 then
put 3 into quad
else if x < 0 and y >= 0 then
put 2 into quad
else if x >= 0 and y < 0 then
put 4 into quad
else
put 1 into quad
end if
switch quad
case 1
if sumThetaPhi <= theta then
put sumThetaPhi - theta into phi
else
put 360 - theta + sumThetaPhi into phi
end if
break
case 2
if sumThetaPhi < 0 then
put 180 + sumThetaPhi into sumThetaPhi
put sumThetaPhi - theta into phi
break
case 3
put 180 + sumThetaPhi into sumThetaPhi
put sumThetaPhi - theta into phi
break
case 4
put 360 + sumThetaPhi into sumThetaPhi
put sumThetaPhi - theta into phi
break
end switch
# phi is angle in degrees with respect to xp,yp coordinates of line
between mouse & origin
# xxx except something appears to be off somewhere in dot location xxx
put pi*phi/180 into phiRad # phiRad in radians
put a*cos(phiRad) into xp
put b*sin(phiRad) into yp
# x,y are coordinates in xp,yp axis of intersection between ellipse
and line between mouse & origin
put pi*theta/180 into thetaRad
put cos(thetaRad)*(xp - yp*cos(thetaRad)) into x
put yp/cos(thetaRad) + tan(thetaRad)*x into y
# x,y are coordinates in x,y axis of intersection between ellipse and
line between mouse & origin
add xO to x
add yO to y
set the loc of graphic "dot" to round(x), round(y)
end repeat
end mouseDown
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