Skip to content

Latest commit

 

History

History
107 lines (75 loc) · 4.25 KB

homog2d_thresholds.md

File metadata and controls

107 lines (75 loc) · 4.25 KB
Raw

Technical details on thresholds an how to manage them

Manual main page

As this library does not use arbitrary precision arithmetic, it may suffer from the weaknesses of traditional floating-point computation. Thus several thresholds are used to manage numerical issues. They are used in the situations described below.

1 - Situations

  • Checking for parallel lines (see isParallelTo() )is done by computing the angle between the lines. If it is below a threshold, the function returns true. The default value is one thousand of a radian (0.001 rad). This is checked for when computing an intersection point between two lines/segments, for example when attempting to build a point from 2 lines.

  • When attempting to compute a line out of two points, if the distance between the two points is less than thr::nullDistance(), then the library will throw an exception.

  • When attempting to compute the inverse of a homography matrix, if the determinant is less than thr::nullDeter(), the inversion code will throw.

All the thresholds have default values. These can be changed at build time, globally, but the values can also be changed at runtime. However, as they are stored as static variables, you may not have different values in different threads, in case of a multithreading app.

2 - Changing thresholds at build time

You can define values for these thresholds before the "include" line, by assigning a value to a symbol. For example:

#define HOMOG2D_THR_ZERO_DIST 1E-10
#include "homog2d.hpp"

These are the symbols to use:

  • HOMOG2D_THR_ZERO_DIST: default value for null distance, i.e. two points whose distance is less than this value will be considered identical points.
  • HOMOG2D_THR_ZERO_ORTHO_DIST: default value for orthogonal distance.
  • HOMOG2D_THR_ZERO_ANGLE: default value for an angle value to be considered null (value must be given in rad.).
  • HOMOG2D_THR_ZERO_DENOM: default value for a denominator to be considered null. Used mostly when checking points for infinity and when normalizing a matrix.
  • HOMOG2D_THR_ZERO_DETER: default value for a matrix determinant to be considered null, thus the matrix will not be inversed.

3 - Changing thresholds at run time

In your code, these values can be read/written any time, using the same functions. They all lie in the sub-namespace thr:

Example:

auto curr = thr::nullDistance();  // store current value
thr::nullDistance() = 1E-6;       // change value
...                               // do some stuff
thr::nullDistance() = curr;       // restore previous value

There is one function per symbol above:

  • thr::nullDistance()
  • thr::nullOrthogDistance()
  • thr::nullAngleValue()
  • thr::nullDenom()
  • thr::nullDeter()

All the threshold current values can be printed at once with:

thr::printThresholds( std::cout );

4 - What value should I use for the thresholds?

Precision of computation and the associated threshold values greatly depend on the numerical range of your data.

Below is a plot that shows the result of an experiment (code provided). It shows the distance (max and mean value) between a line and the points it was generated with. When you build a line using two points (line = pt1 * pt2), the distance between the computed line and both of the points should be 0. But (as you got it), its not. And that is the distance that is shown on the plot below.

This is done on 1 M random point coordinates, in the range shown on horizontal axis, using double and long double as internal numerical type (HOMOG2D_INUMTYPE).

As expected, the results are directly related to the numerical type used for computations, and are better of approximately 10^3 when using long double.

dtest1_d dtest1_l

To run this yourself and generate the plot:
(requires gnuplot)

$ make dtest1

5 - Further readings

Some material on handling floating-point values.