Co-ordinates

[mahadevan.swamy]

Hi,
I have two circles. I have the co-ordinates and radius of the first
circle and the second circle. The condition that should be checked is,
if the co-ordinates of the second circle is in the range of the first
circles, then it should assign a value (0, 1, or X) based on the
condition.

For example, the co-ordinates and radius of the first circle is (x,y,
r) = (1.080, 3.520, 0.062) and for the second circle, it is (x,y, r) =
(0.922, 3.4411, 0.295). I want to check if the second circle is in the
range on the first circle and if it is in the range, the value should
be 0. If the second circle is out of range, the value should be 1. If
the second circle is blocking the first circle or very closely
touching the first circle, the value should be X. The answer to the
proposed problem should be 0 as I have a picture.

Are there any co-ordinate functions in excel? I would appreciate if
anyone can help me to build a good formula for this problem. Thanks

 

[Bernie Deitrick]

Mahadevan,

Simple algebra: The distance between two points is the square root of the sum of the squares of the
differences between the X values and Y values (Pythagorean Theorom):

With X values in row 1, Y values in row 2, R values in row 3, and values for circle one in column A,
circle 2 in column B:

=IF(SQRT((A1-B1)^2+(A2-B2)^2) = (A3+B3),"Touching", IF(SQRT((A1-B1)^2+(A2-B2)^2) <=
ABS(A3-B3),"Completely Overlapping",IF(SQRT((A1-B1)^2+(A2-B2)^2) < (A3+B3),"Partially Overlapping",
"Separated")))

There are four possible states: not touching, just touching, partially overlapping, completely
overlapping. You can change the strings in the formulas to whatever values you want to return.

HTH,
Bernie
MS Excel MVP

 

[Guest]

1. calculate the distance betwenn the centers of the two circles.
2. if the sum of the radii of the two circles exceeds that distance, the
circles overlap.

 

[mahadevan.swamy]

Hi Bernie,

Thank you for your solution. I have a very complicated problem. The
problem is that I have a big circle which consists of 32 small circles
oriented in different places. These circles are sensors that has to
read a part. When the blueprint of the part is placed on top of these
sensors, these sensors should read the part. This blueprint consists
of holes in the drawing and where ever there is a hole on top of the
sensor, the sensor should read 0 or else a 1. That;s why we were
discussing a small aspect of the problem.

I have a row that consists of X, Y and R coordinates for each hole in
the part and a list of sensors with their X,Y and R coordinates. I am
trying to build a logic that will help me to see whether the sensor is
in the range of the hole and execute decisions to produce some
results. I would like to send my files to you if you want to take a
look at them to understand them better. I would appreciate your help
on this. Thanks

Mahadevan

 

[Bernie Deitrick]

Mahadevan,

You could make a table, with the 'sensor' circle data starting in row 5, in columns B (X
coordinate), C (Y coord), and D (R values). Put the 'hole' circle data, starting in Column E in
rows 2 (X coord), 3 (Y coord), and 4 (R value). (Row 1 and column A could be used for data).

Then in cell E5:

=IF(SQRT(($B5-E$2)^2+($C5-E$3)^2) = ($D5+E$4),"Touching", IF(SQRT(($B5-E$2)^2+($C5-E$3)^2) <=
ABS($D5-E$4),"Completely Overlapping",IF(SQRT(($B5-E$2)^2+($C5-E$3)^2) < ($D5+E$4),"Partially
Overlapping",
"Separated")))

Copy this to match both your sensor and hole data, from E5, to say, E5:AA40, and you will get a
table of values - again, change the strings to whatever numeric values you want to have returned.

HTH,
Bernie
MS Excel MVP

 

[mahadevan.swamy]

Hi Bernie,

Thanks for your unique solution. It helped me a lot. I would like to
know how I can summarize the table of values that I got. For example,
I got a row of 1's, so I want the result to be a 1 for the particular
sensor. If there is 0 or X anywhere in the row, I want the result to
be 0 or X. There can be only one value for the sensor. Is there a
function that will do this job? Thanks for your help

Mahadevan Swamy

 

[Bernie Deitrick]

Mahadevan,

=IF(SUM(E5:AJ5) = 32,1,
IF(ISNUMBER(MATCH(0,E5:AJ5,FALSE)),0,IF(ISNUMBER(MATCH("X",E5:AJ5,FALSE)),"X","Other")))

Should work: - change the E5:AJ5 to the range address, and change the 32 to
the maximum expected number of 1's.

HTH,
Bernie
MS Excel MVP

 

[mahadevan.swamy]

Hi Bernie,

Thanks a ton. I would appreciate your advise on how I can organize my
data structure as I have to do the same thing for 1000 part patterns.
I was hoping to create a function that can scan the part hole co-
ordinates (in one row) and then in another worksheet, report what each
sensor got for the corresponding part number. Is there an easier way
to summarize the sensor findings by performing all mathematical
calculations in one formula? Thanks for your help

Mahadevan Swamy

 

[Bernie Deitrick]

Magadevan,

You could write a macro to take the values from a data table, paste them
into your worksheet with the formula table, do a calculation, then copy the
results into another table. That way, you would not have a HUGE workbook,
and the processing would be relatively quick.

Let me know if you want to do the macro. If you do, I would need to know
your data structure, and how you would want the resulting table organized.
I would suggest three sheets: one for the data table, one for the formula
table, and one for results, though all three could go onto one sheet, in
different areas.

HTH,
Bernie
MS Excel MVP


Hi Bernie,

Thanks a ton. I would appreciate your advise on how I can organize my
data structure as I have to do the same thing for 1000 part patterns.
I was hoping to create a function that can scan the part hole co-
ordinates (in one row) and then in another worksheet, report what each
sensor got for the corresponding part number. Is there an easier way
to summarize the sensor findings by performing all mathematical
calculations in one formula? Thanks for your help

Mahadevan Swamy

 

[mahadevan.swamy]

Hi Bernie,

I haven't told you about two design features (holes) of this part. All
this time, we were discussing about parts having some small holes in
different locations and sensors reading them. The design feature I
haven't told you is that there is a bigger inner hole (pilot bore
hole) in the part and all the small holes (mounting holes, sensor
holes etc..) we were discussing about, are outside of this big hole.
This big hole has the coordinate (0,0,r) always. I have managed to use
your formula for that kind of design and sensors will know whether
they are inside the big hole or outside of it.

The next design is a bit tricky. Some parts consists of this hole.
This hole is called a slot which is connected to the bigger inner hole
(pilot bore hole). There are two kinds of slot. One kind of slot looks
like a semi-circle and a rectangle together that is connected to the
pilot bore hole.If you want a picture of this, I can send it to you. I
am given X, Y, and R coordinate of the semi-circle. I am also given
the absolute reference of this point. The other kind of slot looks
like a wide rectangle but is chamfered in the two corners. For this, I
am given width of the rectangle, radius of the chamfer and distance
from the end of the slot to the orgin. I could consider these slots as
a circle but some area of the hole is omitted which could result
giving wrong values for the sensor, if they are in that area. Is there
a better formula to read these designs?

We will continue our discussion of creating a macro for this later as
I am trying to work on this tricky problem. Thanks

Mahadevan Swamy

 

[Bernie Deitrick]

Mahadevan,

Does the slot have a specific orientation, relative to the origin?

HTH,
Bernie
MS Excel MVP


Hi Bernie,

I haven't told you about two design features (holes) of this part. All
this time, we were discussing about parts having some small holes in
different locations and sensors reading them. The design feature I
haven't told you is that there is a bigger inner hole (pilot bore
hole) in the part and all the small holes (mounting holes, sensor
holes etc..) we were discussing about, are outside of this big hole.
This big hole has the coordinate (0,0,r) always. I have managed to use
your formula for that kind of design and sensors will know whether
they are inside the big hole or outside of it.

The next design is a bit tricky. Some parts consists of this hole.
This hole is called a slot which is connected to the bigger inner hole
(pilot bore hole). There are two kinds of slot. One kind of slot looks
like a semi-circle and a rectangle together that is connected to the
pilot bore hole.If you want a picture of this, I can send it to you. I
am given X, Y, and R coordinate of the semi-circle. I am also given
the absolute reference of this point. The other kind of slot looks
like a wide rectangle but is chamfered in the two corners. For this, I
am given width of the rectangle, radius of the chamfer and distance
from the end of the slot to the orgin. I could consider these slots as
a circle but some area of the hole is omitted which could result
giving wrong values for the sensor, if they are in that area. Is there
a better formula to read these designs?

We will continue our discussion of creating a macro for this later as
I am trying to work on this tricky problem. Thanks

Mahadevan Swamy

 

[Bernie Deitrick]

Mahadevan,

Does the slot have a specific orientation, relative to the origin?

HTH,
Bernie
MS Excel MVP


Hi Bernie,

I haven't told you about two design features (holes) of this part. All
this time, we were discussing about parts having some small holes in
different locations and sensors reading them. The design feature I
haven't told you is that there is a bigger inner hole (pilot bore
hole) in the part and all the small holes (mounting holes, sensor
holes etc..) we were discussing about, are outside of this big hole.
This big hole has the coordinate (0,0,r) always. I have managed to use
your formula for that kind of design and sensors will know whether
they are inside the big hole or outside of it.

The next design is a bit tricky. Some parts consists of this hole.
This hole is called a slot which is connected to the bigger inner hole
(pilot bore hole). There are two kinds of slot. One kind of slot looks
like a semi-circle and a rectangle together that is connected to the
pilot bore hole.If you want a picture of this, I can send it to you. I
am given X, Y, and R coordinate of the semi-circle. I am also given
the absolute reference of this point. The other kind of slot looks
like a wide rectangle but is chamfered in the two corners. For this, I
am given width of the rectangle, radius of the chamfer and distance
from the end of the slot to the orgin. I could consider these slots as
a circle but some area of the hole is omitted which could result
giving wrong values for the sensor, if they are in that area. Is there
a better formula to read these designs?

We will continue our discussion of creating a macro for this later as
I am trying to work on this tricky problem. Thanks

Mahadevan Swamy

 

[mahadevan.swamy]

The slot can be oriented anywhere on the part but it has two types as
I have described in my previous post. I am given the radius relative
to the origin for the first type of slot. This radius is the distance
from the orgin to the center of semi-circle. I have another
information which may or may not be useful. The mounting holes (small
holes outside bigger inner hole) has a center line radius measured
with respect to the origin and the slot cannot extend beyond this
radius (for the rectangle part). Small part of the semi-circle is
extended beyond this radius but I am not given the dimension of how
much it has been extended. This applies to both types of slot. I could
scan this picture and send it to you if you want. Thanks for your
assistance.

Mahadevan Swamy

 

[mahadevan.swamy]

I am also given the angle of slot orientation if that helps.

Mahadevan

 

[Bernie Deitrick]

Mahadevan,

I think you would need the XY coordinates of the 4 courners of the slot.

Do you have that? Or perhaps we could derive it....

Bernie


I am also given the angle of slot orientation if that helps.

Mahadevan

 

[mahadevan.swamy]

It can be easy to find the coordinates of the 4 corners of the
rectangle since I am given the angle in which the slot (center) is
oriented, the width of the slot and the radius of the slot (semi-
circle) from (0,0). Using cosine law, I can find the coordinates of
the corners of the rectangle. Assuming that I am given (x1,y1)......
(x4, y4) for the rectangle how am i going to use this info to see if
the sensor is in that area?

Thanks

Mahadevan Swamy

 

[mahadevan.swamy]

Hi Bernie,

This is the logic I have written for the slots being oriented at
different angles.
The way I have numbered is starting with the top right corner of the
rectangle and then top left corner of the rectangle.

Conditions for getting 0

For 0 < angle < 90,
x3<x<x2
y3<y<y2
x4<x<x1
y4<y<y1

For 90<angle<180
x1< x < x4
y4<y<y1
x2<x<x3
y3<y<y2

For 180<angle<270
x1<x<x4
y1<y<y4
x2<x<x3
y2<y<y3

For 270<angle<360
x4<x<x1
y1<y<y4
x2<x<x2
y2<y<y3

The two sets conditions are written for each angle if the sensor is
out of range for the circle and in the range of rectangle at two
places (left and right). In the data structure that you have given me,
I could put up a condition where if the row for slot is equal to 0,
then prevent executing the function that I have written for slot or
else if the sensor is in the range of the circle and rectangle, then
execute the conditions that I have given above. What is your
suggestion?

Thanks
Mahadevan Swamy

 

[Bernie Deitrick]

Mahadevan,

Your logic won't work for rectangles (slots) that are not orthogonal to the
axes.

I will write a formula that uses Excel's FORECAST function to compute the
actual values of the slot's edges at the X and Y coordinates of the
sensor.... I've been meaning to do that, but I haven't had time.... so just
hang in there a bit...

Bernie

Hi Bernie,

This is the logic I have written for the slots being oriented at
different angles.
The way I have numbered is starting with the top right corner of the
rectangle and then top left corner of the rectangle.

Conditions for getting 0

For 0 < angle < 90,
x3<x<x2
y3<y<y2
x4<x<x1
y4<y<y1

For 90<angle<180
x1< x < x4
y4<y<y1
x2<x<x3
y3<y<y2

For 180<angle<270
x1<x<x4
y1<y<y4
x2<x<x3
y2<y<y3

For 270<angle<360
x4<x<x1
y1<y<y4
x2<x<x2
y2<y<y3

The two sets conditions are written for each angle if the sensor is
out of range for the circle and in the range of rectangle at two
places (left and right). In the data structure that you have given me,
I could put up a condition where if the row for slot is equal to 0,
then prevent executing the function that I have written for slot or
else if the sensor is in the range of the circle and rectangle, then
execute the conditions that I have given above. What is your
suggestion?

Thanks
Mahadevan Swamy

 

[mahadevan.swamy]

Hi Bernie,

Your condition: - SQRT(($B5-E$2)^2+($C5-E$3)^2) <= ABS($D5-E
$4),"Completely Overlapping". In this condition, you are saying if the
sensor touches the hole from the inside, then that is a 0 and in the
other condition, you are saying that if the sensor is touching the
egde of the hole then that would be an X (touching). For both of these
conditions, it should be an X. So my formula would be OR(IF(SQRT(($B5-E
$2)^2+($C5-E$3)^2) = ABS($D5-E$4),"X"), IF(SQRT(($B5-E$2)^2+($C5-E
$3)^2) = $D5+E$4,"X")). Is this right?

If the sensor is beyond the range of the circle, it would be SQRT((x2-
x1)^2+(y2-y1)^2)> ABS(r2-r1). r2 is the radius of the sensor and r1 is
the radius of the hole. Do you agree?

How is the formula for the slot coming along? There are some
parameters that could be used for the calculation and they are: angle
of the slot orientation, length from (0,0) to the end of the slot,
width of the slot and radius of the chamfer. For cast slot (the radius
of the chamfer would be a quarter of the circle and for machined slot,
the radius of chamfer would be 1/2 of the circle completely.

Thanks
Mahadevan Swamy

 

[mahadevan.swamy]

Hi Bernie,

These are the conditions that I have for the sensor to read the
holes.

For the result of 0, I have SQRT((x2-x1)^2 + (y2-y1)^2) < abs(r2-r1)
---------------- (uncovered)

For result of X, I have SQRT((x2-x1)^2 + (y2-y1)^2) = abs(r2-r1)
--------------------- (touching from the inside)
AND SQRT((x2-x1)^2 + (y2-y1)^2) <= r1+r2 ----------------(Touching
from outside and partially blocked)

However, I have a small problem. When the edge of the hole is very
close to the sensor by 30 thou, it should be regarded as X (in other
words, it should not exceed 0.03 or else it would be a 1 or a 0
depending on whether the sensor in inside the hole or outside of it).
Can you suggest a solution for that? Thanks

Mahadevan