ISO 16610-62:2023 PDF

Geometrical product specifications (GPS) — Filtration — Part 62: Linear areal filters: spline filters

First page of standard ISO 16610-62:2023

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Title (English):

ISO 16610-62:2023

Geometrical product specifications (GPS) — Filtration — Part 62: Linear areal filters: spline filters

Document status:: Active
Format:: Electronic (PDF)
Number of pages:: 10
Publication date:: February 17, 2023
Edition:: ISO IS 16610 edition 1 version 1
ICS:: 17.040.20

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Description (English):

This document specifies the characteristics of a linear areal spline filter with a global shape retainment.

Technical details

Technical committee: ISO/TC 213 - Dimensional and geometrical product specifications and verification
SKU: ISO 16610-62:2023

Abstract

Overview

ISO 16610-62:2023 - "Geometrical product specifications (GPS) - Filtration - Part 62: Linear areal filters: spline filters" specifies the characteristics of a linear areal spline filter designed to separate long‑ and short‑wave components of surface topography while providing global shape retainment. It defines the cubic spline low‑pass areal filter for both planar and cylindrical surfaces, gives filter formulas for uniformly sampled and distorted grids, and describes parameters that control smoothing and transfer behavior.

Keywords: ISO 16610-62:2023, spline filters, linear areal filters, GPS filtration, cubic spline areal filter, shape retainment.

Key topics

Filter concept and scope
- Defines a linear areal spline filter as an areal extension of the profile spline filter for surface topography maps.
- Covers both linear planar and linear cylindrical (periodic) implementations.
Filter formulation
- Presents the low‑pass filter formula for cubic spline areal filters using matrix transformations.
- Includes two transformation matrices (for x and y directions) built from identity, differentiation matrices and scalar parameters.
Control parameters
- Regularization parameter (related to cut‑off wavelength and sampling intervals) - controls smoothing (waviness) of the low‑passed result.
- Tension parameter (β) - controls slope of the transfer function and degree of curvature following; β ranges between 0 and 1 and affects shape retainment (β = 0 gives minimum tension; a documented intermediate β produces Gaussian‑like characteristics).
Differentiation matrices (P and Q)
- Matrices represent discretized first and second derivatives (gradients and curvatures).
- Document specifies main/first/second off‑diagonals and special handling for planar vs cylindrical boundary conditions.
Distorted sampling grids
- Extends the model to non‑uniform/distorted grids by replacing matrices with appropriately dimensioned tensors and using average sampling intervals.
Additional content
- Transmission characteristics, filter designation rules, and informative annexes relating the spline filter to the filtration matrix model and GPS matrix model.

Applications and users

Practical use: separation of roughness and waviness in surface metrology, processing CMM or areal topography data, and preparing measurement data for specification and verification.
Typical users:
- Metrologists and quality engineers in precision manufacturing (automotive, aerospace, medical devices).
- Measurement software developers and instrument vendors implementing GPS‑compliant filtration.
- Standards bodies and researchers working on surface texture characterization.

Related standards

ISO 16610 series (overview and related parts): ISO 16610‑1, ISO 16610‑21 (Gaussian profile), ISO 16610‑22 (spline profile), ISO 16610‑60/61 (areal basics and Gaussian areal).
GPS framework: ISO 14638, ISO 8015, ISO 14253‑1, and ISO/IEC Guide 99 (VIM).

For implementation details, formulae and numerical parameter relations (regularization/tension), refer to the full ISO 16610-62:2023 document.

Related standards

Standards mentioned in the description

Abstract

Overview

Keywords: ISO 16610-62:2023, spline filters, linear areal filters, GPS filtration, cubic spline areal filter, shape retainment.

Key topics

Filter concept and scope
- Defines a linear areal spline filter as an areal extension of the profile spline filter for surface topography maps.
- Covers both linear planar and linear cylindrical (periodic) implementations.
Filter formulation
- Presents the low‑pass filter formula for cubic spline areal filters using matrix transformations.
- Includes two transformation matrices (for x and y directions) built from identity, differentiation matrices and scalar parameters.
Control parameters
- Regularization parameter (related to cut‑off wavelength and sampling intervals) - controls smoothing (waviness) of the low‑passed result.
- Tension parameter (β) - controls slope of the transfer function and degree of curvature following; β ranges between 0 and 1 and affects shape retainment (β = 0 gives minimum tension; a documented intermediate β produces Gaussian‑like characteristics).
Differentiation matrices (P and Q)
- Matrices represent discretized first and second derivatives (gradients and curvatures).
- Document specifies main/first/second off‑diagonals and special handling for planar vs cylindrical boundary conditions.
Distorted sampling grids
- Extends the model to non‑uniform/distorted grids by replacing matrices with appropriately dimensioned tensors and using average sampling intervals.
Additional content
- Transmission characteristics, filter designation rules, and informative annexes relating the spline filter to the filtration matrix model and GPS matrix model.

Applications and users

Practical use: separation of roughness and waviness in surface metrology, processing CMM or areal topography data, and preparing measurement data for specification and verification.
Typical users:
- Metrologists and quality engineers in precision manufacturing (automotive, aerospace, medical devices).
- Measurement software developers and instrument vendors implementing GPS‑compliant filtration.
- Standards bodies and researchers working on surface texture characterization.

Related standards

ISO 16610 series (overview and related parts): ISO 16610‑1, ISO 16610‑21 (Gaussian profile), ISO 16610‑22 (spline profile), ISO 16610‑60/61 (areal basics and Gaussian areal).
GPS framework: ISO 14638, ISO 8015, ISO 14253‑1, and ISO/IEC Guide 99 (VIM).

For implementation details, formulae and numerical parameter relations (regularization/tension), refer to the full ISO 16610-62:2023 document.

ISO 16610-62:2023 PDF

Technical details

Abstract

Overview

Key topics

Applications and users

Related standards

Related standards

Abstract

Overview

Key topics

Applications and users

Related standards

Related standards

Geometrical product specifications (GPS) - Filtration - Part 22: Linear profile filters: Spline filters (ISO…

Geometrical product specifications (GPS) - Filtration - Part 1: Overview and basic concepts (ISO 16610-1:2015)

Geometrical product specifications (GPS) - Filtration - Part 21: Linear profile filters: Gaussian filters (IS…

Geometrical product specification (GPS) - Masterplan (ISO 14638:2015)

Geometrical product specifications (GPS) - Fundamentals - Concepts, principles and rules (ISO 8015:2011)

Geometrical product specifications (GPS) - Inspection by measurement of workpieces and measuring equipment -…