HAS-Motion Software Documentation

User Tools

Site Tools

You are here: Main Page » visual3d » documentation » pipeline » expressions » Least Squares Fitting of Data
visual3d:documentation:pipeline:expressions:least_squares_fitting_of_data

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
visual3d:documentation:pipeline:expressions:least_squares_fitting_of_data [2024/06/19 12:49] – sgrangervisual3d:documentation:pipeline:expressions:least_squares_fitting_of_data [2025/01/24 18:53] (current) – [Best Fit Plane] wikisysop
Line 1: Line 1:
-{{{{{{{{this page contains a list of all functions that are used to find a line or plane of best fit to your data.+===== Least Squares Fitting of Data =====
  
-===== best fit plane =====+This page contains a list of all of [[visual3d:documentation:pipeline:expressions:expressions_overview|Evaluate_Expression]]'s functions that are used to find a line or plane of best fit to your data.
  
-**best_fit_plane**(signal, start_event_signal, end_event_signal) - find a plane that fits the path of a point from a start event to an end event.+==== Best Fit Plane ====
  
-[[[https://en.wikipedia.org/wiki/plane_%28geometry%29#point-normal_form_and_general_form_of_the_equation_of_a_plane|the resulting plane is defined by 4 components]]] +**Best_Fit_Plane**(signal, start_event_signal, end_event_signal) - Finds a plane that fits the path of a point from a start event to an end event. [[https://en.wikipedia.org/wiki/Plane_%28geometry%29#Point-normal_form_and_general_form_of_the_equation_of_a_plane|The resulting plane is defined by 4 components]].
-example: compute a best_plane_fit for one signal across a range of frames +
-**evaluate_expression** +
-/expression=best_fit_plane(current_signal,event_label::original::start,event_label::original::end) +
-/signal_types=target +
-/signal_folder=original +
-/signal_names=lsk_1 +
-/result_types=metric +
-/result_folders=processed +
-/result_name=lsk1_plane +
-/apply_as_suffix_to_signal_name=true +
-**;** +
-example: compute a best_plane_fit for multiple signals at each frame of data +
-**evaluate_expression** +
-/expression=best_fit_plane(current_signal) +
-/signal_types=target +
-/signal_folder=original +
-/signal_names=lsk_1+lsk_2+lsk_3 +
-/result_types=derived +
-/result_folders=processed +
-/result_name=lsk_plane +
-/apply_as_suffix_to_signal_name=true +
-**;** +
-===== best fit circle =====+
  
-**best_fit_circle**(signal, start_event_signal, end_event_signal)+The general form of the equation of a plane in 3D is ax+by+cz+d = 0 where 𝑎, 𝑏, and 𝑐 are the components of the normal vector which is perpendicular to the plane or any vector parallel to the plane.
  
-fit a 2d circle to the path of a signal. +If (𝑥0,𝑦0,𝑧0)is a point that lies on the plane, then 𝑑=−(𝑎𝑥0+𝑏𝑦0+𝑐𝑧0) and as 𝑎𝑥+𝑏𝑦+𝑐𝑧−(𝑎𝑥0+𝑏𝑦0+𝑐𝑧0)=0.
-the algorithm computes a best fit plane to the data, rotates this plane into a principal plane, computes the center and radius, the rotates these values back into the original plane. +
-the result is 4 components; the x,y,z location of the origin and the radius. +
-\\+
  
 +The result of the Best_Fit_Plane function is a signal with the fource components (a,b,c,d)
  
-===== best fit sphere =====+<code> 
 +! Example: Compute a Best_Plane_Fit for one signal across a range of frames 
 +Evaluate_Expression 
 +/EXPRESSION=Best_Fit_Plane(CURRENT_SIGNAL,EVENT_LABEL::ORIGINAL::START,EVENT_LABEL::ORIGINAL::END) 
 +/SIGNAL_TYPES=TARGET 
 +/SIGNAL_FOLDER=ORIGINAL 
 +/SIGNAL_NAMES=LSK_1 
 +/RESULT_TYPES=METRIC 
 +/RESULT_FOLDERS=PROCESSED 
 +/RESULT_NAME=LSK1_PLANE 
 +/APPLY_AS_SUFFIX_TO_SIGNAL_NAME=TRUE 
 +; 
 +</code>
  
-**best_fit_sphere**(signal,start_event_signal,end_event_signal)+<code> 
 +! Example: Compute a Best_Plane_Fit for multiple signals at each frame of data 
 +Evaluate_Expression 
 +/EXPRESSION=Best_Fit_Plane(CURRENT_SIGNAL) 
 +/SIGNAL_TYPES=TARGET 
 +/SIGNAL_FOLDER=ORIGINAL 
 +/SIGNAL_NAMES=LSK_1+LSK_2+LSK_3 
 +/RESULT_TYPES=DERIVED 
 +/RESULT_FOLDERS=PROCESSED 
 +/RESULT_NAME=LSK_PLANE 
 +/APPLY_AS_SUFFIX_TO_SIGNAL_NAME=TRUE 
 +; 
 +</code>
  
-example : fit a sphere to 6 points on a diamond +==== Best Fit Circle ====
-create 6 targets representing the vertices+
  
-[[visual3d:documentation:pipeline:signal_commands:create_target|create_target]] +**Best_Fit_Circle**(signal, start_event_signal, end_event_signal) - Fits a 2D circle to the path of a signal.
-/signal_names=v1 +
-! /signal_description= +
-/expression=vector((0.5+0*frame_numbers::original::frames),0,0) +
-! /include_calfile=false +
-**;** +
-[[visual3d:documentation:pipeline:signal_commands:create_target|create_target]] +
-/signal_names=v2 +
-! /signal_description= +
-/expression=vector((-0.5+0*frame_numbers::original::frames),0,0) +
-! /include_calfile=false +
-**;** +
-[[visual3d:documentation:pipeline:signal_commands:create_target|create_target]] +
-/signal_names=v3 +
-! /signal_description= +
-/expression=vector((0,0.5+0*frame_numbers::original::frames),0) +
-! /include_calfile=false +
-**;** +
-[[visual3d:documentation:pipeline:signal_commands:create_target|create_target]] +
-/signal_names=v4 +
-! /signal_description= +
-/expression=vector((0,-0.5+0*frame_numbers::original::frames),0) +
-! /include_calfile=false +
-**;** +
-[[visual3d:documentation:pipeline:signal_commands:create_target|create_target]] +
-/signal_names=v5 +
-! /signal_description= +
-/expression=vector((0,0,0.5+0*frame_numbers::original::frames)) +
-! /include_calfile=false +
-**;** +
-[[visual3d:documentation:pipeline:signal_commands:create_target|create_target]] +
-/signal_names=v6 +
-! /signal_description= +
-/expression=vector((0,0,-0.5+0*frame_numbers::original::frames)) +
-! /include_calfile=false +
-**;** +
-**evaluate_expression** +
-/expression=best_fit_sphere(current_signal) +
-/signal_types=target +
-/signal_folder=original +
-/signal_names=v1+v2+v3+v4+v5+v6 +
-/result_types=derived +
-! /result_folders=processed +
-/result_name=sphere +
-! /apply_as_suffix_to_signal_name=false +
-**;** +
-note that targets are created and the sphere computed has each target on its surface. sphere1.jpgsphere6view.jpg+
  
-example : create a target where each frame is on a random location on the surface of a sphere of radius 1 +The algorithm computes a best fit plane to the data, rotates this plane into a principal plane, computes the center and radius, the rotates these values back into the original plane. The result is 4 components: 
-**evaluate_expression** +  - the origin's X-coordinate; 
-/expression=rand(-pi(),pi(),frame_numbers::original::frames) +  - the origin's Y-coordinate; 
-/result_types=derived +  - the origin's Z-coordinate; and 
-/result_folders=radius +  - the radius.
-/result_name=vertical +
-! /apply_as_suffix_to_signal_name=false +
-**;** +
-**evaluate_expression** +
-/expression=rand(0,2*pi(),frame_numbers::original::frames) +
-/result_types=derived +
-/result_folders=radius +
-/result_name=horizontal +
-! /apply_as_suffix_to_signal_name=false +
-**;** +
-[[visual3d:documentation:pipeline:signal_commands:create_target|create_target]] +
-/signal_names=sphere +
-! /signal_description= +
-/expression=vector( +
-cos(derived::radius::vertical)*cos(derived::radius::horizontal), +
--cos(derived::radius::vertical)*sin(derived::radius::horizontal), +
-sin(derived::radius::vertical)) +
-! /include_calfile=false +
-**;** +
-**evaluate_expression** +
-/expression=best_fit_sphere(current_signal) +
-/signal_types=target +
-/signal_folder=original +
-/signal_names=sphere +
-/result_types=derived +
-! /result_folders=processed +
-/result_name=sphere +
-! /apply_as_suffix_to_signal_name=false +
-**;** +
-random8view.jpg +
-sphererandom.jpg +
-===== simple linear regression =====+
  
-**simple_linear_regression**(signal1, signal2, start_event, end_event); - fit a signal to a line. y = mx + b.+==== Best Fit Sphere ====
  
-signal2 = m signal1 + b +**Best_Fit_Sphere**(signal,start_event_signal,end_event_signal) - Fits a 3D sphere to the path of a signal.
-an explanation of the calculation can be found [[visual3d:documentation:statistics:compute_linear_regression|here]] or [[[https://en.wikipedia.org/wiki/simple_linear_regression|here]]] +
-signal1 and signal2 are one component signals +
-resulting metric signal contains 6 components +
-slope = m -> component 1 +
-intercept = b -> component 2 +
-siga = uncertainty in m -> component 3 +
-sigb = uncertainty in b -> component 4 +
-chi2 = chi square -> component 5 +
-q = the r^2 statistic -> component 6+
  
-}}}}}}}}+<code> 
 +! Example : Fit a sphere to 6 points on a DIAMOND 
 + 
 +! Create 6 TARGETS representing the Vertices 
 +Create_Target 
 +/SIGNAL_NAMES=V1 
 +! /SIGNAL_DESCRIPTION= 
 +/EXPRESSION=VECTOR((0.5+0*FRAME_NUMBERS::ORIGINAL::FRAMES),0,0) 
 +! /INCLUDE_CALFILE=FALSE 
 +; 
 + 
 +Create_Target 
 +/SIGNAL_NAMES=V2 
 +! /SIGNAL_DESCRIPTION= 
 +/EXPRESSION=VECTOR((-0.5+0*FRAME_NUMBERS::ORIGINAL::FRAMES),0,0) 
 +! /INCLUDE_CALFILE=FALSE 
 +; 
 + 
 +Create_Target 
 +/SIGNAL_NAMES=V3 
 +! /SIGNAL_DESCRIPTION= 
 +/EXPRESSION=VECTOR((0,0.5+0*FRAME_NUMBERS::ORIGINAL::FRAMES),0) 
 +! /INCLUDE_CALFILE=FALSE 
 +; 
 + 
 +Create_Target 
 +/SIGNAL_NAMES=V4 
 +! /SIGNAL_DESCRIPTION= 
 +/EXPRESSION=VECTOR((0,-0.5+0*FRAME_NUMBERS::ORIGINAL::FRAMES),0) 
 +! /INCLUDE_CALFILE=FALSE 
 +; 
 + 
 +Create_Target 
 +/SIGNAL_NAMES=V5 
 +! /SIGNAL_DESCRIPTION= 
 +/EXPRESSION=VECTOR((0,0,0.5+0*FRAME_NUMBERS::ORIGINAL::FRAMES)) 
 +! /INCLUDE_CALFILE=FALSE 
 +; 
 + 
 +Create_Target 
 +/SIGNAL_NAMES=V6 
 +! /SIGNAL_DESCRIPTION= 
 +/EXPRESSION=VECTOR((0,0,-0.5+0*FRAME_NUMBERS::ORIGINAL::FRAMES)) 
 +! /INCLUDE_CALFILE=FALSE 
 +; 
 + 
 +Evaluate_Expression 
 +/EXPRESSION=Best_Fit_Sphere(CURRENT_SIGNAL) 
 +/SIGNAL_TYPES=TARGET 
 +/SIGNAL_FOLDER=ORIGINAL 
 +/SIGNAL_NAMES=V1+V2+V3+V4+V5+V6 
 +/RESULT_TYPES=DERIVED 
 +! /RESULT_FOLDERS=PROCESSED 
 +/RESULT_NAME=SPHERE 
 +! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE 
 +; 
 +</code> 
 + 
 +Note that TARGETS are created and the sphere computed has each TARGET on its surface. 
 + 
 +{{:Sphere1.jpg}}{{:sphere6view.jpg}} 
 + 
 +<code> 
 +! Example : Create a TARGET where each frame is on a random location on the surface of a sphere of radius 1 
 +Evaluate_Expression 
 +/EXPRESSION=RAND(-PI(),PI(),FRAME_NUMBERS::ORIGINAL::FRAMES) 
 +/RESULT_TYPES=DERIVED 
 +/RESULT_FOLDERS=RADIUS 
 +/RESULT_NAME=VERTICAL 
 +! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE 
 +; 
 + 
 +Evaluate_Expression 
 +/EXPRESSION=RAND(0,2*PI(),FRAME_NUMBERS::ORIGINAL::FRAMES) 
 +/RESULT_TYPES=DERIVED 
 +/RESULT_FOLDERS=RADIUS 
 +/RESULT_NAME=HORIZONTAL 
 +! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE 
 +; 
 + 
 +Create_Target 
 +/SIGNAL_NAMES=SPHERE 
 +! /SIGNAL_DESCRIPTION= 
 +/EXPRESSION=VECTOR( 
 +COS(DERIVED::RADIUS::VERTICAL)*COS(DERIVED::RADIUS::HORIZONTAL), 
 +-COS(DERIVED::RADIUS::VERTICAL)*SIN(DERIVED::RADIUS::HORIZONTAL), 
 +SIN(DERIVED::RADIUS::VERTICAL)) 
 +! /INCLUDE_CALFILE=FALSE 
 +; 
 + 
 +Evaluate_Expression 
 +/EXPRESSION=Best_Fit_Sphere(CURRENT_SIGNAL) 
 +/SIGNAL_TYPES=TARGET 
 +/SIGNAL_FOLDER=ORIGINAL 
 +/SIGNAL_NAMES=SPHERE 
 +/RESULT_TYPES=DERIVED 
 +! /RESULT_FOLDERS=PROCESSED 
 +/RESULT_NAME=SPHERE 
 +! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=FALSE 
 +; 
 +</code> 
 + 
 +{{:random8view.jpg}} 
 +{{:sphereRandom.jpg}} 
 + 
 +==== Simple Linear Regression ==== 
 + 
 +**Simple_Linear_Regression**(signal1, signal2, start_event, end_event); - Fits a signal to a line given by the equation Y = mX + b where 
 + 
 +<code> 
 +Signal = m Signal1 + b 
 +</code> 
 + 
 +An explanation of the calculation can be found [[Visual3D:Documentation:Statistics:Compute_Linear_Regression|here]] or [[https://en.wikipedia.org/wiki/Simple_linear_regression|here]]. 
 + 
 +Signal1 and Signal2 are both one-component signals and the resulting METRIC contains 6 components: 
 +  - Slope = m -> Component 1 
 +  - Intercept = b -> Component 2 
 +  - Siga = uncertainty in m -> Component 3 
 +  - Sigb = uncertainty in b -> Component 4 
 +  - Chi2 = chi square -> Component 5 
 +  - Q = The R^2 statistic -> Component 6
visual3d/documentation/pipeline/expressions/least_squares_fitting_of_data.1718801397.txt.gz · Last modified: 2024/06/19 12:49 by sgranger