Carl Zeiss Industrial Metrology
Algorithms
July 2003
Engineering Conference
Richard Knebel
The new scanning generation
Carl Zeiss © 2003 Page 1
Carl Zeiss IMT
Algorithms
Minimum
Circumscribed Maximum
Circle Inscribed Circle
Minimum Zone Single
Circle Points
Real
Contour
Sequence of Gaussian
Scanning Points Least
(continuous probing) Squares
Circle
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Carl Zeiss IMT
Why Least Squares ?
• Provides a consistent,
stable result
• Consistently provides the Single
Points
– Wrong Size
– Wrong Location
– Wrong Form
Real
Contour
Gaussian
Least
Squares
Circle
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Carl Zeiss IMT
Why Maximum Inscribed ?
• Provides the correct result Maximum
for Inscribed Circle
– Size
– Location
• On internal diameters
• When used with enough
data density
Real
Contour
• However it is not as stable a
Least Squares because ?? Sequence of
Scanning Points
– It fits on extreme points (continuous probing)
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Carl Zeiss IMT
Why Minimum Circumscribed ?
Minimum
• Provides the correct result Circumscribed
for Circle
– Size
– Location
• On external diameters
• When used with enough
data density
Real
Contour
• However it is not as stable a
Least Squares because ?? Sequence of
Scanning Points
– It fits on extreme points (continuous probing)
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Carl Zeiss IMT
Why Minimum Zone ?
• Provides the correct result
for Minimum Zone
Circle
– Form
• When used with enough
data density
Real
Contour
• However it is not as stable a
Least Squares because ?? Sequence of
Scanning Points
– It fits on extreme points (continuous probing)
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Carl Zeiss IMT
What about Inner and Outer Tangential ?
• What’s the difference between Outer Tangential and
Maximum Inscribed on an internal diameter ?
Nothing !
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Carl Zeiss IMT
What about Inner and Outer Tangential ?
• What’s the difference between Outer Tangential and
Minimum Circumscribed on an external diameter ?
Nothing !
Carl Zeiss © 2003 Page 8
Carl Zeiss IMT
What about Inner and Outer Tangential ?
• What’s the difference between Inner Tangential and
Minimum Circumscribed on an internal diameter ?
Minimum
Circumscribed
• Nothing ! Circle
• Is this functional ?
• No !
• When might you use it ? Real
Contour
• To determine if there is enough material on a casting so
that it will cleanup during machining or to evaluate wall
thickness
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Carl Zeiss IMT
What about Inner and Outer Tangential ?
• What’s the difference between Inner Tangential and
Maximum Inscribed on an external diameter ?
Maximum
Inscribed Circle
• Nothing !
• Is this functional ?
• No !
• When might you use it ?
Real
Contour
• To determine if there is enough material on a casting so
that it will cleanup during machining or to evaluate wall
thickness
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Carl Zeiss IMT
So why do we have Inner and Outer Tangential ?
• Because it is more
descriptive for Planes
and Lines
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Carl Zeiss IMT
So lets generalize the math
• We have Gaussian Least Squares fits which minimize the
square root of the sum of the squared errors
– In this type of fit all data points have the same weight in determining
the fit
– There is absolutely nothing functional about this type of fit
Single
Points
Real
Contour
Gaussian
Least
Squares
Circle
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Carl Zeiss IMT
So lets generalize the math
• We have extrema fits (Inner and Outer Tangential, Max
Inscribed, Min Circumscribed) which fit on the high points
of the feature
– In this type of fit only the high points have any weight in determining
the fit
– This is absolutely functional fitting for size and location like when
mating a plane against a granite surface plate, or finding the slip fit
pin that just fits into a bore Maximum
Inscribed Circle
Minimum
Circumscribed
Circle
Real
Contour
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Carl Zeiss IMT
So lets generalize the math
• We have minimum zone fits which equally balance the
high and low point of the feature
– In this type of fit only the high point and low point have any weight in
determining the fit
– This is absolutely functional fitting for form analysis
Minimum Zone
Circle
Real
Contour
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Carl Zeiss IMT
Summary
• Know the basic best use of
each algorithm Minimum
Circumscribed Maximum
Circle Inscribed Circle
• Understand the potential
difference (pros and cons)
each algorithm can provide Single
Points
• Apply the algorithm that
meets the needs of the
customer and application
accordingly
• There is no one simple rule Real
Contour
that can define what to use
when, as an Applications Gaussian
Engineer you must help Sequence of
Scanning Points Least
decide what is best on a (continuous probing) Squares
case-by-case basis Circle
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