Page 85 - DCAP313_LAB_ON_COMPUTER_GRAPHICS

Unit 5: Implementing Ellipse Algorithm

then return (–1, ERROR_ELLIPSE_PARAMETERS) :DATA CHECK Notes
do if (|φ| > 2
then φ← (φ modulo 2) :BRING φ INTO –2≤φ < 2 (?)
do if (|X 1 |/A > 2)
then X1 ← –A
X10 ← cos(φ)*(X 1 – H) + sin(φ)*(Y 1 – K)
Y 10 ← –sin(φ)*(X 1 – H) + cos(φ)*(Y 1 – K)
X 20 ← cos(φ)*(X 2 – H) + sin(φ)*(Y 2 – K)
Y 20 ← –sin(φ)*(X 2 – H) + cos(φ)*(Y 2 – K)
do if (|X 20 – X 10 | > ε) :LINE IS NOT VERTICAL
then m ← (Y 20 – Y 10 )/(X 20 – X 10 ) :STORE QUADRATIC COEFFICIENTS

a ← (B 2 + (A*m)2)/A 2
b ← (2.0*(Y 10 *m – m 2 *X 10 ))
c ← (Y 102 – 2.0*m*Y 10 *X 10 + (m*X 10 )2 – B 2 )

else if (|Y 20 – Y 10 | > ε) :LINE IS NOT HORIZONTAL
then m ← (X 20 – X 10 )/(Y 20 – Y 10 ) :STORE QUADRATIC COEFFS

a ← (A 2 + (B*m)2)/B 2
b ← (2.0*(X 10 *m – m 2 *Y 10 ))
c ← (X 102 – 2.0*m*Y 10 *X 10 + (m*Y 10 )2 – A 2 )
else return (–1, ERROR_LINE_POINTS) :LINE POINTS TOO CLOSE
discrim ← b2 – 4.0*a*c
do if (discrim < 0.0):LINE DOES NOT CROSS ELLIPSE
then return (0, NO_INTERSECT)

else if (discrim > 0.0): TWO INTERSECTION POINTS
then root1 ← (–b – sqrt (discrim))/(2.0*a)
root2 ← (–b + sqrt (discrim))/ (2.0*a)
else return (0, TANGENT) :LINE TANGENT TO ELLIPSE
do if (|X 20 – X 10 | > ε) :ROOTS ARE X-VALUES
then do if (X 10 < X 20 ) :ORDER PTS SAME AS LINE DIRECTION
then x 1 ← root 1
x 2 ← root 2
else x 1 ← root 2

x 2 ← root 1
else do if (Y 10 < Y 20 ) :ROOTS ARE Y-VALUES
then y 1 ← root 1 :ORDER PTS SAME AS LINE DIRECTION

y 2 ← root 2
else y 1 ← root 2
y 2 ← root 1
(Area,Code) ← ELLIPSE_SEGMENT (A,B,x 1 ,y 1 ,x 2 ,y 2 )

LOVELY PROFESSIONAL UNIVERSITY 79