hello all
anyone know what is the Best fit and what is 2D-fit ?
and what difference between them?

Best fit is where you "float" the model you create from the actual data points obtained from a part against the controling model. You try and adjust the overlaying process such that you get the created model to "best fit" the referance model.

For 2-D fit you remove one axis of "float" and just work in the X and Y axis ( but could be any other two axis)

:2cents:

Most scientific calculators can perform a simple linear regression (Y=MX+B where M is the slope and B is the Y intercept) which “best fits” a line to a given set of coordinate points when the X and Y coordinate values for each point are entered. This “best fit” line is located and oriented among the points so that the sum of the squared residual perpendicular distance of all points from the line is minimized; hence it is often referred to as “least squares best fit”.

These regression functions can be adapted to other simple geometric shapes such as circles, spheres, cones or more exotic shapes like torus contours, ellipses, etc. Like andygr replied an entire cloud of measured points can be compared to any given geometric form by “floating” adjusting the X,Y,Z translations and I,J,K axis rotations so that the least squared residuals “best fit” of the points to the given geometric form or “model” is achieved.

A 2D-fit simply uses 2 of the coordinate translation values and their corresponding axis rotation variables where a 3D fit uses all of them.

Paul

My background is coordinate metrology and geometric modeling. A bestfit can be done by transforming a collected data set in reference to the design model to reevaluate deviations. A typical 3D transform has six degrees of freedom: rotations about and translations along the XYZ coordinate axis. Other factors such as scaling (for CTE) can also be incorporated. A 2D bestfit constrains the transformation to a plane.

A typical bestfit uses the least squares method (sum of the errors squared) which basically tries to achieve the most 'good'. A bad point or observation does not unduly sway the solution. This is the cheapest computational method. Another method I use is to minimize the range of the deviations in order to determine whether the data set falls within a tolerance band (profile). You can also start assigning weights (levels of importance) to different points having different tolerances or in order to constrain certain features (datums).

All bestfit algorithms I create hinge on one thing: creating a function having a single numerical value as it's result and trying to minimize it. Constraints can be implemented anywhere along the way.

You are 'fitting' to a preconceived notion as to what 'best' is. Best general least squares fit? Best fit to reduce tolerance used? Best fit to minimize rework? Best fit to assure attach holes line up allowing a mating surface to float with the solution?

Least squares approach is generally the safest. Also the most widely used and understood.