polishing sink oval

dear all,

i have a diffucelt question (trying to motivate the experts here)
i want to polish an oval marble sink.
i calculated the movement, by splitting the edge of the oval sink and mid point into two arc.
then i moving along the angle from 0-360.
which works for me.
can be view the process here : https://www.youtube.com/watch?v=qpobzqI7tSQ

but i need now to deal with the a,b,c that will be in offset of 20deg to the surface i going:
an example of what i need to achived is here : https://www.youtube.com/watch?v=P76tcOgVqjs
this was done by teaching the points and moving along them.
i want to do all the math with calculated points.

tried to figure it out with geometric opreator, with no success

the code as follow:

DEF OvalSink(SinkBot:IN)
DECL E6POS SinkBot
DECL POS OriCorrSink, OriCorrSinkMid


;for oval sink calc


DECL REAL pi ;pi value
DECL REAL t ;radius
DECL REAL calcX ;calculated x 
DECL REAL calcY ;calculated y 
DECL REAL calcXmid ;calculated middle x point
DECL REAL calcYmid ;calculated middle y point
DECL REAL a ;a in elipse the width of sink
DECL REAL b ;b in elipse the height of sink
DECL INT maxOri ;maximum orientation of the tool in the bowl


t=0 ; zero degree
pi=3.1415 ;pi value
a=100 ;sink width
b=70 ;sink hight
OriCorrSink={X 0, Y 0, Z 0, A 0, B 0, C 0}
OriCorrSinkMid={X 0, Y 0, Z 0, A 0, B 0, C 0}
maxOri = 40


$BASE=BASE_DATA[3]
$TOOL=TOOL_DATA[3]
;go to center sink will be end point 
EndPoint = SinkBot ;<== getting the value from main program
PTP EndPoint ; move to middle of sink


FOR counter = 0 TO 360 STEP 18
   ;calculate x,y for start point
   t=counter
   calcX = a*(cos(t))
   calcY = b*(sin(t))
   OriCorrSink.C = maxOri*(cos(t))
   OriCorrSink.B = maxOri*(cos(t))
   calcXmid = (a/2)*(cos(t))
   calcYmid = (a/2)*(sin(t))
   OriCorrSinkMid.C = (maxOri/2)*(cos(t))
   OriCorrSinkMid.B = (maxOri/2)*(cos(t))
   StartPoint = EndPoint
   StartPoint.X = StartPoint.X + calcX
   StartPoint.Y = StartPoint.Y + calcY
   StartPoint = StartPoint:OriCorrSink
   StartPoint.Z = StartPoint.Z - 150   ;go down , sink depth
   midPoint.X = EndPoint.X + calcXmid
   midPoint.Y = EndPoint.Y + calcYmid
   midPoint = midPoint:OriCorrSinkMid
   ;move to sink elipse point
   CIRC midPoint,StartPoint
   ;move back to center
   CIRC midPoint,EndPoint
   StartPoint = $NULLFRAME   
ENDFOR
PTP XHOME
END

but i getting:
midpoint.z a b c value invalid

when i try to look the midpoint values
i getting only x and y values

what i doing wrong?

CA 360? please explain.
i need to polish an ovel sink, where alpha and beta are diffrent.
what does the CA 360 does?

i can live with the 360 times.
but how i make the tool orinated to the surface, in some deg?
i need to polish the sink with the end of the polish tool, while looking at the other end not to touch the surface.
i don't know even how to start it, since i know the robot can go in x,y,z , but i will make him change correctly his angle?

i uploaded two video that showing the one i have and the desired one.

the sink is part of the whole surface.
it's not a marble , but an industrial marbel, which you cast into a template.
after it's dry out, you need to polish from 100grid paper to 600grid (extra fine) paper.

the problem is more complex then you think.
since it's casted marble, there are diffrent heights up to 1cm, while there is a thick cover of 2mm on the top of the marble.
it's a very complex software.

but i think i will do something else, i will take aurdino board , connect to it a kinect which have camera and depth. get geomatric data of the sink, and using Euler equastion, i calculate the polish offset.

hope it will work for me

band sand will do the same problem as the tool i have now.
i using band sand to polish square sinks. and it's working great

the kinect is rough resultion, i agree with that, but in a perfect world, i would have a 3d laser maserment, and the robot move by cad program.
but in the real world, the customer nor the boss want to pay any extra cent, deal with what you have, they say, you have also additional budget of 250$.
i think i will use it to buy a ferrari (remote control ferrari).