Characterisation of freeform, structured surfaces in T-spline spaces and its applications

Abstract

In advanced manufacturing, surface topographical designs with deterministic freeform and embedded structures have proven to contain effective, additive functionalities. These surfaces need to be geometrically characterised regarding the designed form and structures. However, this is problematic since existing characterisation techniques such as polynomial form removal, Gaussian/spline/wavelet filtration, field-based statistical parameterisation, spectral and fractal analysis do not provide satisfying results. In this paper, we, therefore, propose to characterise the complex surfaces in T-spline spaces, i.e. basis spline spaces along with T-junctions, using an efficient T-spline fitting algorithm. Several case studies show that the proposed method is compatible and has notable potentials for the challenging characterisation tasks, including non-Euclidean freeform removal, edge-reserving filtration with multiscale analysis, scattered data interpolation and smoothing, and smart large-data downsampling or compression.

Stitching Locally Fitted T-Splines for Fast Fitting of Large-Scale Freeform Point Clouds

“…However, the final T-spline optimization process reconsiders the local support characteristics of CPs and geometrical continuities between split patches, with the result that initially obtained fitting accuracy cannot hold to the end. An accuracy degeneration phenomenon shown in Figure 5 b indicates that the final resulting T-spline’s root-mean-square error (RMSE) is usually twice the value before a final patch connection, and it could be fourfold or even larger than a pre-set maximum fitting error threshold [ 10 ]. Therefore, specifying a smaller error threshold is usually required in the initial split fitting to satisfy a final accuracy requirement.…”

“…At present, advanced optical scanning has enabled the acquisition of over ten million 3D point clouds within a second [ 8 , 9 ]. For precision metrology of surfaces with complex freeform geometry, dense point cloud acquisition has become an ordinary measurement routine, using which a denoised point cloud, polygon mesh, or CAD model is finally fitted [ 10 ]. The spline technique has clearly become an indispensable part of surface fitting in point cloud data processing due to its many advantages such as smoothness, mathematical feasibility, and controllability [ 11 ].…”

Multiscale assessment of additively manufactured free-form surfaces

“…There is a number of factors that affect theoretical differences and the assessed model [17,18]. When analysing the current state of the art, one can note that there are currently ongoing works assessing the quality of created free-form surfaces [19,20]. The authors of [21] evaluated the accuracy of reconstructing free-form surfaces in CMM/CAD/CAM/CNC systems.…”

Multilevel T-spline Approximation for Scattered Observations with Application to Land Remote Sensing

“…This challenge is enhanced by the addition of a smoothing term; [14] showed exemplarily that the condition number of the stiffness matrix for HB, truncated HB and LR B-splines is linked to increasing refinement levels in the context of isogeometric analysis. An adaptive procedure was proposed recently by [34] based on a local LS fitting method to face that challenge. Unfortunately, the fitting of complex geometries still produced ripples in the presence of noise and outliers.…”