find the stretch-rotation of a geometric object
find the homology of a geometric object
find the spiral-rotation of a geometric object
StretchRotation(Q, P, O, theta, dir, k)
homology(Q, P, O, theta, dir, k)
SpiralRotation(Q, P, O, theta, dir, k)
the name of the object to be created
point which is the center of the homology
number which is the angle of the homology
name which is either clockwise or counterclockwise
number which is the ratio of the homology
Let O be a fixed point in the plane, k a given nonzero real number, theta and dir denote a given sensed angle. By the homology ( or stretch-rotation, or spiral-rotation) H⁡O,k,θ we mean the product R⁡O,thetaH⁡O,k where R⁡O,θ,dir is the rotation with respect to O an angle theta in direction dir and H⁡O,k is the dilatation with respect to the center O and ratio k.
Point O is called the center of the homology, k the ratio of the homology, theta and dir the angle of the homology.
For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))
The command with(geometry,StretchRotation) allows the use of the abbreviated form of this command.
define the parabola with vertex at (0,0) and focus at (0,1/2)
draw⁡p1⁡color=green,style=LINE,thickness=2,numpoints=50,p2,p3,p4,p5,style=POINT,numpoints=200,color=brown,title=`homology of a parabola`
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