pith. sign in

arxiv: 2606.31764 · v1 · pith:ISBKBLVRnew · submitted 2026-06-30 · 💻 cs.GR · cs.CV

NURBS Splatting: A Unified Differentiable Rendering Framework for Vector Graphics

Jingye Qiu , Shizhe Zhou This is my paper

Pith reviewed 2026-07-01 02:24 UTC · model grok-4.3

classification 💻 cs.GR cs.CV
keywords NURBSdifferentiable renderingvector graphicsGaussian splattingspline renderingcurve vectorizationplanar curves
0
0 comments X

The pith

Representing NURBS curves as sampled Gaussian fields reformulates vector graphics rendering as a stable differentiable accumulation process.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a method to make rendering of planar rational splines differentiable by converting them into continuous fields of Gaussians. Sampling occurs both along the curve's parameter domain and inside closed regions, turning the process into smooth accumulation rather than direct analytic evaluation. This approach supports features like rational weights, non-uniform knots, long splines, and region filling that prior analytic methods struggle with. A sympathetic reader would care because vector graphics appear in design, reconstruction, and abstraction tasks where gradient stability directly affects optimization quality and flexibility.

Core claim

NURBS Splatting represents planar rational curves as continuous Gaussian fields. By sampling Gaussians along the curve parameter domain and inside closed regions, rendering is reformulated as a smooth accumulation process with stable gradients. The method naturally supports long splines, rational weights, non-uniform knots, and closed-region filling, and is demonstrated on calligraphy reconstruction, vectorization frameworks, and long-spline image abstraction.

What carries the argument

NURBS Splatting as continuous Gaussian fields sampled along the parameter domain and inside closed regions, which converts analytic curve rendering into differentiable accumulation.

If this is right

  • Calligraphy reconstruction becomes feasible with improved stability over analytic baselines.
  • Vectorization frameworks gain the ability to handle rational weights and non-uniform knots without custom gradient fixes.
  • Long-spline image abstraction produces higher-quality results because the accumulation process avoids gradient instability.
  • Closed regions can be filled differentiably by sampling inside boundaries rather than boundary-only evaluation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same sampling idea might extend to other parametric curve families if their parameter domains admit similar Gaussian placement.
  • Optimization loops that currently avoid long splines due to instability could now incorporate them directly.
  • The framework suggests a general pattern where any curve representation could be turned into a splattable field for differentiability.

Load-bearing premise

That discrete sampling of Gaussians along the NURBS parameter domain yields gradients stable enough and faithful enough to the analytic curve for the shown reconstruction tasks.

What would settle it

A side-by-side optimization run on long splines where the Gaussian method produces visibly worse reconstruction error or diverges while an analytic baseline converges.

Figures

Figures reproduced from arXiv: 2606.31764 by Jingye Qiu, Shizhe Zhou.

Figure 1
Figure 1. Figure 1: We optimize NURBS parameters (control points Pi, weights wi, knot intervals τi) by sampling isotropic Gaussians along the curve and interior. These primitives are rendered via a differentiable tile-based rasterizer, enabling end-to-end optimization through image and geometric losses. support B-splines but do not introduce rational weights or non-uniform knots. Consequently, differentiable renderers cannot … view at source ↗
Figure 2
Figure 2. Figure 2: Visualization of grid-step annealing. The grid resolution progressively increases, allowing coarse-to-fine optimization [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Single-stroke area-filling results. Letters are stylized with different style images; digits use coverage loss only (no stylization). where Limg is the distance-weighted MSE loss, L 3 deriv is the third-order derivative smoothing loss, and Lxing is a self-crossing penalty adapted from LIVE that pe￾nalizes control-point configurations whose consecutive segments reverse winding direction. Results are present… view at source ↗
Figure 4
Figure 4. Figure 4: Image abstraction with semantic stylization. Style images are inset in the bot￾tom corners of the inputs. Our method matches stylization quality while running 1.27× faster (single NVIDIA RTX 4090, 512×512, 300 iterations). where ˆϵ(xt, t, y) is the predicted denoising direction of the frozen diffusion model for a latent xt at time step t, ϵ is the sampled noise, and w(t) is a weighting function dependent o… view at source ↗
Figure 5
Figure 5. Figure 5: Rendering comparison on three diagnostic cases. Bézier Splatting (BS) shows blurred edges on thick strokes (left pair), spike artifacts near high-curvature regions (middle pair, local crop), and spikes at filled-region junctions (right pair). Bézier splines are equivalently converted to NURBS for fair geometric comparison [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Qualitative comparison of calligraphy reconstruction. Top row: Japanese char￾acters. Bottom row: Chinese characters. Our method better preserves stroke trajectories and width variations compared to the baseline [2] [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Qualitative comparison of vector reconstruction. Our method faithfully recon￾structs complex facial expressions and fine details where the DiffVG-based baseline tends to fail. 6 Conclusion We presented NURBS Splatting, the first differentiable rendering framework capable of optimizing rational B-splines in 2D image space. By representing curves and filled regions as continuous Gaussian fields, our method u… view at source ↗
read the original abstract

Differentiable rendering of planar rational splines remains largely underexplored, despite their widespread use in vector graphics and design. Existing differentiable vector renderers primarily focus on B\'ezier curves and rely on analytic rasterization, which can suffer from gradient instability and limited flexibility. We propose NURBS Splatting, a unified framework that represents planar rational curves as continuous Gaussian fields. By sampling Gaussians along the curve parameter domain and inside closed regions, rendering is reformulated as a smooth accumulation process with stable gradients. Our method naturally supports long splines, rational weights, non-uniform knots, and closed-region filling. We demonstrate its effectiveness in calligraphy reconstruction, vectorization frameworks, and long-spline image abstraction, showing improved stability and reconstruction quality over existing approaches.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper proposes NURBS Splatting, a unified differentiable rendering framework for planar rational splines. It represents NURBS curves as continuous Gaussian fields by sampling Gaussians along the curve parameter domain and inside closed regions, reformulating rendering as a smooth accumulation process. The method is claimed to yield stable gradients while naturally supporting long splines, rational weights, non-uniform knots, and closed-region filling. Effectiveness is demonstrated on calligraphy reconstruction, vectorization frameworks, and long-spline image abstraction, with reported improvements in stability and reconstruction quality over existing approaches.

Significance. If the stability and faithfulness claims hold under quantitative validation, the approach could offer a practical alternative to analytic rasterization for differentiable vector graphics, enabling more robust optimization in applications involving complex NURBS geometry.

major comments (1)
  1. [Abstract] Abstract: The central claim that discrete Gaussian sampling along the NURBS parameter domain produces gradients that remain stable and faithful to the analytic curve (including for rational weights, non-uniform knots, and long splines) is load-bearing but unsupported by any derivation details, error bounds on approximation error (as a function of sample count, Gaussian variance, or curvature), or side-by-side comparisons against analytic rasterization. Without these, the stability advantage cannot be assessed.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the single major comment below, acknowledging the need for additional support on the stability claims while clarifying the empirical evidence already present.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that discrete Gaussian sampling along the NURBS parameter domain produces gradients that remain stable and faithful to the analytic curve (including for rational weights, non-uniform knots, and long splines) is load-bearing but unsupported by any derivation details, error bounds on approximation error (as a function of sample count, Gaussian variance, or curvature), or side-by-side comparisons against analytic rasterization. Without these, the stability advantage cannot be assessed.

    Authors: We agree that the manuscript does not provide a formal derivation of error bounds on the approximation error (as a function of sample count, Gaussian variance, or curvature) or a theoretical analysis of gradient faithfulness to the analytic curve. The stability claim rests on the formulation of rendering as a smooth accumulation of Gaussians (detailed in Section 3), which ensures differentiability by construction, together with empirical demonstrations across the experiments. These include successful optimization on long splines, rational weights, and non-uniform knots (Sections 4.1–4.3), with quantitative improvements in reconstruction quality and stability over analytic baselines. Visual and numerical side-by-side comparisons of rendered results and optimization trajectories are included in the main figures and supplementary material. We will add a dedicated subsection on approximation properties and expanded gradient-stability comparisons in the revision. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is a modeling reformulation independent of its outputs

full rationale

The paper's core step is to represent NURBS curves as sampled Gaussian fields and reformulate rendering as accumulation; this is an explicit modeling choice presented in the abstract as a direct reformulation, not a quantity fitted or defined in terms of its own predictions. No equations, self-citations, or uniqueness claims appear in the provided text that would reduce the claimed stable gradients or support for rational weights/non-uniform knots back to the method's own inputs by construction. The approach is self-contained as a proposed framework with external demonstrations, meeting the criteria for an honest non-finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The method rests on the modeling choice that Gaussian sampling along the parameter domain is a sufficient continuous approximation; no free parameters, axioms, or invented entities are explicitly listed in the abstract.

pith-pipeline@v0.9.1-grok · 5657 in / 1007 out tokens · 38199 ms · 2026-07-01T02:24:10.275755+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

53 extracted references · 35 canonical work pages · 2 internal anchors

  1. [1]

    ACM Trans

    Berio, D., Leymarie, F.F., Asente, P., Echevarria, J.: StrokeStyles: Stroke-based Segmentation and Stylization of Fonts. ACM Trans. Graph.41(3), 28:1–28:21 (Apr 2022).https://doi.org/10.1145/3505246

    work page doi:10.1145/3505246 2022

  2. [2]

    ACM Trans

    Berio, D., Stroh, M., Calinon, S., Fol Leymarie, F., Deussen, O., Shamir, A.: Neural Image Abstraction using Long Smoothing B-Splines. ACM Trans. Graph.44(6), 225:1–225:11 (Dec 2025).https://doi.org/10.1145/3763345

    work page doi:10.1145/3763345 2025

  3. [3]

    CVGIP: Image Understanding55(3), 329–338 (May 1992).https://doi.org/10

    Brandt, J.W., Algazi, V.R.: Continuous skeleton computation by Voronoi diagram. CVGIP: Image Understanding55(3), 329–338 (May 1992).https://doi.org/10. 1016/1049-9660(92)90030-7

    1992

  4. [4]

    Chakraborty, S., Batra, V., Phogat, A., Jain, V., Ranawat, J.S., Dhingra, S., Wampler, K., Fisher, M., Lukáč, M.: Image Vectorization via Gradient Recon- struction. Comput. Graph. Forum44(2) (May 2025).https://doi.org/10.1111/ cgf.70055

    2025

  5. [5]

    In: Peytavie, A., Bosch, C

    Chen,X.,Lian,Z.,Tang,Y.,Xiao,J.:Anautomaticstrokeextractionmethodusing manifold learning. In: Peytavie, A., Bosch, C. (eds.) Proceedings of the European AssociationforComputerGraphics:ShortPapers.pp.65–68.EG’17,Eurographics Association, Goslar, DEU (Apr 2017).https://doi.org/10.2312/egsh.20171016

    work page doi:10.2312/egsh.20171016 2017

  6. [6]

    IMA Journal of Applied Math- ematics10(2), 134–149 (Oct 1972).https://doi.org/10.1093/imamat/10.2.134

    Cox, M.G.: The Numerical Evaluation of B-Splines. IMA Journal of Applied Math- ematics10(2), 134–149 (Oct 1972).https://doi.org/10.1093/imamat/10.2.134

    work page doi:10.1093/imamat/10.2.134 1972

  7. [7]

    Journal of Approximation Theory6(1), 50–62 (Jul 1972).https://doi.org/10.1016/0021-9045(72)90080-9

    de Boor, C.: On calculating with B-splines. Journal of Approximation Theory6(1), 50–62 (Jul 1972).https://doi.org/10.1016/0021-9045(72)90080-9

    work page doi:10.1016/0021-9045(72)90080-9 1972

  8. [8]

    Computer-Aided Design146, 103199 (May 2022).https://doi.org/10.1016/j.cad.2022.103199

    Deva Prasad, A., Balu, A., Shah, H., Sarkar, S., Hegde, C., Krishnamurthy, A.: NURBS-Diff: A Differentiable Programming Module for NURBS. Computer-Aided Design146, 103199 (May 2022).https://doi.org/10.1016/j.cad.2022.103199

    work page doi:10.1016/j.cad.2022.103199 2022

  9. [10]

    Morgan Kaufmann (Sep 2007).https://doi.org/10.1016/B978-1-55860-737-8.X5000-5

    Farin, G.: Curves and Surfaces for CAGD: A Practical Guide. Morgan Kaufmann (Sep 2007).https://doi.org/10.1016/B978-1-55860-737-8.X5000-5

    work page doi:10.1016/b978-1-55860-737-8.x5000-5 2007

  10. [11]

    https://www.foundertype.com/index.php/FontInfo/index/id/6583.html, accessed: 2026-02-28

    Founder Type Foundry: Founder Ouyang Xun Regular Script Font. https://www.foundertype.com/index.php/FontInfo/index/id/6583.html, accessed: 2026-02-28

    2026

  11. [12]

    In: Koyejo, S., Mohamed, S., Agarwal, A., Belgrave, D., Cho, K., Oh, A

    Frans, K., Soros, L., Witkowski, O.: CLIPDraw: Exploring text-to-drawing synthe- sis through language-image encoders. In: Koyejo, S., Mohamed, S., Agarwal, A., Belgrave, D., Cho, K., Oh, A. (eds.) Advances in Neural Information Processing Systems. vol. 35, pp. 5207–5218. Curran Associates, Inc. (2022)

    2022

  12. [13]

    https://github.com/googlefonts/noto-emoji, accessed: 2026-03-05

    Google Fonts: Noto Emoji. https://github.com/googlefonts/noto-emoji, accessed: 2026-03-05

    2026

  13. [14]

    Proceedings of the AAAI Conference on Artifi- cial Intelligence38(3), 2148–2156 (Mar 2024).https://doi.org/10.1609/aaai

    Hirschorn, O., Jevnisek, A., Avidan, S.: Optimize & Reduce: A Top-Down Ap- proach for Image Vectorization. Proceedings of the AAAI Conference on Artifi- cial Intelligence38(3), 2148–2156 (Mar 2024).https://doi.org/10.1609/aaai. v38i3.27987

    work page doi:10.1609/aaai 2024

  14. [15]

    In: ACM SIGGRAPH 2024 Conference Pa- pers

    Huang, B., Yu, Z., Chen, A., Geiger, A., Gao, S.: 2D Gaussian Splatting for Geo- metrically Accurate Radiance Fields. In: ACM SIGGRAPH 2024 Conference Pa- pers. pp. 1–11. SIGGRAPH ’24, Association for Computing Machinery, New York, NY, USA (Jul 2024).https://doi.org/10.1145/3641519.3657428

    work page doi:10.1145/3641519.3657428 2024

  15. [16]

    Computer Methods in 16 J

    Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in 16 J. Qiu and S. Zhou Applied Mechanics and Engineering194(39), 4135–4195 (Oct 2005).https:// doi.org/10.1016/j.cma.2004.10.008

    work page doi:10.1016/j.cma.2004.10.008 2005

  16. [17]

    ACM Trans

    Iluz, S., Vinker, Y., Hertz, A., Berio, D., Cohen-Or, D., Shamir, A.: Word-As- Image for Semantic Typography. ACM Trans. Graph.42(4), 151:1–151:11 (Jul 2023).https://doi.org/10.1145/3592123

    work page doi:10.1145/3592123 2023

  17. [18]

    In: 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

    Jain, A., Xie, A., Abbeel, P.: VectorFusion: Text-to-SVG by Abstracting Pixel- Based Diffusion Models. In: 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 1911–1920 (Jun 2023).https://doi.org/10. 1109/CVPR52729.2023.00190

    arXiv 2023

  18. [19]

    In: Sarhangi, R., Moody, R.V

    Kaplan, C.S., Bosch, R.: TSP Art. In: Sarhangi, R., Moody, R.V. (eds.) Renais- sance Banff: Mathematics, Music, Art, Culture. pp. 301–308. Bridges Conference, Southwestern College, Winfield, Kansas (2005)

    2005

  19. [20]

    https://karu- k.booth.pm/items/2985842, accessed: 2026-02-28

    Keikan & Midnight Garden: Yoppa Fude Font. https://karu- k.booth.pm/items/2985842, accessed: 2026-02-28

    arXiv 2026

  20. [21]

    ACM Trans

    Kerbl, B., Kopanas, G., Leimkuehler, T., Drettakis, G.: 3D Gaussian Splatting for Real-Time Radiance Field Rendering. ACM Trans. Graph.42(4), 139:1–139:14 (Aug 2023).https://doi.org/10.1145/3592433

    work page doi:10.1145/3592433 2023

  21. [22]

    In: 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

    Kwon, G., Ye, J.C.: CLIPstyler: Image Style Transfer with a Single Text Condition. In: 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 18041–18050 (Jun 2022).https://doi.org/10.1109/CVPR52688. 2022.01753

    work page doi:10.1109/cvpr52688 2022

  22. [23]

    ACM Trans

    Li, T.M., Lukáč, M., Gharbi, M., Ragan-Kelley, J.: Differentiable vector graphics rasterization for editing and learning. ACM Trans. Graph.39(6), 193:1–193:15 (Dec 2020).https://doi.org/10.1145/3414685.3417871

    work page doi:10.1145/3414685.3417871 2020

  23. [25]

    In: Belgrave, D., Zhang, C., Lin, H., Pascanu, R., Koniusz, P., Ghassemi, M., Chen, N

    Liu, X., Zhou, C., Zhao, N., Huang, S.: Bézier splatting for fast and differen- tiable vector graphics rendering. In: Belgrave, D., Zhang, C., Lin, H., Pascanu, R., Koniusz, P., Ghassemi, M., Chen, N. (eds.) Advances in Neural Information Processing Systems. vol. 38, pp. 51528–51559. Curran Associates, Inc. (2025)

    2025

  24. [26]

    ACM Trans

    Loop, C., Blinn, J.: Resolution independent curve rendering using programmable graphics hardware. ACM Trans. Graph.24(3), 1000–1009 (Jul 2005).https:// doi.org/10.1145/1073204.1073303

    work page doi:10.1145/1073204.1073303 2005

  25. [27]

    Journal of Computer Science and Technology10(1), 42–52 (1995).https://doi.org/10.1007/BF02939521

    Ma, X., Pan, Z., Zhang, F.: The automatic generation of chinese outline font based on stroke extraction. Journal of Computer Science and Technology10(1), 42–52 (1995).https://doi.org/10.1007/BF02939521

    work page doi:10.1007/bf02939521 1995

  26. [28]

    In: IEEE/CVF Con- ference on Computer Vision and Pattern Recognition, CVPR 2022, New Orleans, LA, USA, June 18-24, 2022

    Ma, X., Zhou, Y., Xu, X., Sun, B., Filev, V., Orlov, N., Fu, Y., Shi, H.: Towards Layer-wise Image Vectorization. In: 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 16293–16302. IEEE, New Orleans, LA, USA (Jun 2022).https://doi.org/10.1109/CVPR52688.2022.01583

    work page doi:10.1109/cvpr52688.2022.01583 2022

  27. [29]

    In: 2025 IEEE/CVF International Con- ference on Computer Vision (ICCV)

    Ma, Z., Jiang, J., Chen, Y., Zhang, L.: BézierGS: Dynamic Urban Scene Re- construction with Bézier Curve Gaussian Splatting. In: 2025 IEEE/CVF Inter- national Conference on Computer Vision (ICCV). pp. 25519–25528 (Oct 2025). https://doi.org/10.1109/ICCV51701.2025.02367

    work page doi:10.1109/iccv51701.2025.02367 2025

  28. [30]

    Magne, T., Sorkine-Hornung, O.: Single-Line Drawing Vectorization. Comput. Graph. Forum44(7), e70228 (2025).https://doi.org/10.1111/cgf.70228

    work page doi:10.1111/cgf.70228 2025

  29. [31]

    MinistryofEducationofthePeople’sRepublicofChina:TableofGeneralStandard Chinese Characters (2013)

    2013

  30. [32]

    Springer-Verlag, Berlin, Hei- delberg (1997) NURBS Splatting 17

    Piegl, L., Tiller, W.: The NURBS Book (2nd Ed.). Springer-Verlag, Berlin, Hei- delberg (1997) NURBS Splatting 17

    1997

  31. [33]

    Computer-Aided Design22(4), 241– 245 (May 1990).https://doi.org/10.1016/0010-4485(90)90053-F

    Pottmann, H.: Smooth curves under tension. Computer-Aided Design22(4), 241– 245 (May 1990).https://doi.org/10.1016/0010-4485(90)90053-F

    work page doi:10.1016/0010-4485(90)90053-f 1990

  32. [34]

    In: 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

    Thamizharasan, V., Liu, D., Agarwal, S., Fisher, M., Gharbi, M., Wang, O., Ja- cobson, A., Kalogerakis, E.: VecFusion: Vector Font Generation with Diffusion. In: 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 7943–7952 (Jun 2024).https://doi.org/10.1109/CVPR52733.2024. 00759

    work page doi:10.1109/cvpr52733.2024 2024

  33. [35]

    IEEE Transactions on Visualization and Computer Graphics31(12), 10711–10722 (Dec 2025).https://doi.org/10

    Tian, Y., Liu, M., Jiang, H., Tu, Y., Su, D.: SketchRefiner: Text-Guided Sketch Refinement Through Latent Diffusion Models. IEEE Transactions on Visualization and Computer Graphics31(12), 10711–10722 (Dec 2025).https://doi.org/10. 1109/TVCG.2025.3613388

    arXiv 2025

  34. [36]

    In: ACM SIGGRAPH 2024 Conference Papers

    Tojo, K., Shamir, A., Bickel, B., Umetani, N.: Fabricable 3D Wire Art. In: ACM SIGGRAPH 2024 Conference Papers. pp. 1–11. SIGGRAPH ’24, Association for Computing Machinery, New York, NY, USA (Jul 2024).https://doi.org/10. 1145/3641519.3657453

    arXiv 2024

  35. [37]

    ACM Trans

    Vinker, Y., Pajouheshgar, E., Bo, J.Y., Bachmann, R.C., Bermano, A.H., Cohen- Or, D., Zamir, A., Shamir, A.: CLIPasso: Semantically-aware object sketching. ACM Trans. Graph.41(4), 86:1–86:11 (Jul 2022).https://doi.org/10.1145/ 3528223.3530068

    arXiv 2022

  36. [38]

    ACM Trans

    Wang, Y., Lian, Z.: DeepVecFont: Synthesizing high-quality vector fonts via dual- modality learning. ACM Trans. Graph.40(6), 265:1–265:15 (Dec 2021).https: //doi.org/10.1145/3478513.3480488

    work page doi:10.1145/3478513.3480488 2021

  37. [39]

    In���� �������� ���������� �� �������� ������ ��� ������� ����������� ������

    Wang, Y., Wang, Y., Yu, L., Zhu, Y., Lian, Z.: DeepVecFont-v2: Exploiting Trans- formers to Synthesize Vector Fonts with Higher Quality. In: 2023 IEEE/CVF Con- ference on Computer Vision and Pattern Recognition (CVPR). pp. 18320–18328 (Jun 2023).https://doi.org/10.1109/CVPR52729.2023.01757

    work page doi:10.1109/cvpr52729.2023.01757 2023

  38. [40]

    In: 2025 IEEE/CVF Conference on Com- puter Vision and Pattern Recognition, CVPR 2025, Nashville, TN, USA, June 11- 15, 2025

    Wang, Z., Huang, J., Sun, Z., Gong, Y., Cohen-Or, D., Lu, M.: Layered Image Vectorization via Semantic Simplification. In: 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 7728–7738 (Jun 2025). https://doi.org/10.1109/CVPR52734.2025.00724

    work page doi:10.1109/cvpr52734.2025.00724 2025

  39. [41]

    Wang, Z., Lu, M.: Image-Space Collage and Packing with Differentiable Rendering. In: Proceedings of the Special Interest Group on Computer Graphics and Interac- tiveTechniquesConferenceConferencePapers.AssociationforComputingMachin- ery, New York, NY, USA (2025).https://doi.org/10.1145/3721238.3730690

    work page doi:10.1145/3721238.3730690 2025

  40. [42]

    ACM Trans

    Worchel, M., Alexa, M.: Differentiable Rendering of Parametric Geometry. ACM Trans. Graph.42(6), 232:1–232:18 (Dec 2023).https :// doi.org /10 .1145/ 3618387

    2023

  41. [43]

    Zaletel, and Joel E

    Wu, S.J., Yang, C.Y., Hsu, J.Y.j.: CalliGAN: Style and Structure-aware Chinese CalligraphyCharacterGenerator(May2020).https://doi.org/10.48550/arXiv. 2005.12500

    work page internal anchor Pith review doi:10.48550/arxiv 2005

  42. [44]

    In: Oh, A., Naumann, T., Globerson, A., Saenko, K., Hardt, M., Levine, S

    Xing, X., Wang, C., Zhou, H., Zhang, J., Yu, Q., Xu, D.: DiffSketcher: Text Guided Vector Sketch Synthesis through Latent Diffusion Models. In: Oh, A., Naumann, T., Globerson, A., Saenko, K., Hardt, M., Levine, S. (eds.) Advances in Neural Information Processing Systems. vol. 36, pp. 15869–15889. Curran Associates, Inc. (2023)

    2023

  43. [45]

    In: 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

    Xing, X., Zhou, H., Wang, C., Zhang, J., Xu, D., Yu, Q.: SVGDreamer: Text Guided SVG Generation with Diffusion Model. In: 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 4546–4555 (Jun 2024). https://doi.org/10.1109/CVPR52733.2024.00435 18 J. Qiu and S. Zhou

    work page doi:10.1109/cvpr52733.2024.00435 2024

  44. [46]

    ACM Trans.Graph.43(4),119:1–119:14(Jul2024).https://doi.org/10.1145/3658129

    Xu, X., Lambourne, J., Jayaraman, P., Wang, Z., Willis, K., Furukawa, Y.: Brep- Gen: A B-rep Generative Diffusion Model with Structured Latent Geometry. ACM Trans.Graph.43(4),119:1–119:14(Jul2024).https://doi.org/10.1145/3658129

    work page doi:10.1145/3658129

  45. [47]

    IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models

    Ye, H., Zhang, J., Liu, S., Han, X., Yang, W.: IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models (Aug 2023).https://doi. org/10.48550/arXiv.2308.06721

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2308.06721 2023

  46. [48]

    In: The Thirteenth Inter- national Conference on Learning Representations (2025),https://openreview

    Yoon, J., Han, S., Oh, J., Lee, M.: SplineGS: Learning Smooth Trajectories in Gaussian Splatting for Dynamic Scene Reconstruction. In: The Thirteenth Inter- national Conference on Learning Representations (2025),https://openreview. net/forum?id=tMG6btjBfd, accessed: 2026-06-26

    2025

  47. [49]

    org/10.1609/aaai.v35i4.16438

    Zeng, J., Chen, Q., Liu, Y., Wang, M., Yao, Y.: StrokeGAN: Reducing Mode CollapseinChineseFontGenerationviaStrokeEncoding.ProceedingsoftheAAAI Conference on Artificial Intelligence35(4), 3270–3277 (May 2021).https://doi. org/10.1609/aaai.v35i4.16438

    work page doi:10.1609/aaai.v35i4.16438 2021

  48. [50]

    In: 2023 IEEE/CVF International Conference on Computer Vision (ICCV)

    Zhang, L., Rao, A., Agrawala, M.: Adding Conditional Control to Text-to-Image Diffusion Models. In: 2023 IEEE/CVF International Conference on Computer Vi- sion (ICCV). pp. 3813–3824 (Oct 2023).https://doi.org/10.1109/ICCV51070. 2023.00355

    work page doi:10.1109/iccv51070 2023

  49. [51]

    In: 2018 IEEE/CVF Con- ference on Computer Vision and Pattern Recognition

    Zhang, R., Isola, P., Efros, A.A., Shechtman, E., Wang, O.: The Unreasonable Effectiveness of Deep Features as a Perceptual Metric. In: 2018 IEEE/CVF Con- ference on Computer Vision and Pattern Recognition. pp. 586–595 (Jun 2018). https://doi.org/10.1109/CVPR.2018.00068

    work page doi:10.1109/cvpr.2018.00068 2018

  50. [52]

    In: Proceedings of the 3rd Interna- tional Workshop on Multimodal and Responsible Affective Computing

    Zhang, X., Liu, Z., Liu, J., Li, X., Qi, M.: SketchDancing: A Text-Driven Frame- work for Vector Sketch Animation Generation. In: Proceedings of the 3rd Interna- tional Workshop on Multimodal and Responsible Affective Computing. pp. 128–

  51. [53]

    MRAC ’25, Association for Computing Machinery, New York, NY, USA (Oct 2025).https://doi.org/10.1145/3746270.3760235

    work page doi:10.1145/3746270.3760235 2025

  52. [54]

    In: Leonardis, A., Ricci, E., Roth, S., Russakovsky, O., Sattler, T., Varol, G

    Zhang, X., Ge, X., Xu, T., He, D., Wang, Y., Qin, H., Lu, G., Geng, J., Zhang, J.: GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaus- sian Splatting. In: Leonardis, A., Ricci, E., Roth, S., Russakovsky, O., Sattler, T., Varol, G. (eds.) Computer Vision – ECCV 2024. pp. 327–345. Springer Nature Switzerland, Cham (2025).https://doi.org...

    work page doi:10.1007/978-3-031-72673-6_18 2024

  53. [55]

    Calligraphy Recon- struction

    Zou, Q., Zhu, L., Wu, J., Yang, Z.: SplineGen: Approximating unorganized points through generative AI. Computer-Aided Design178, 103809 (Jan 2025).https: //doi.org/10.1016/j.cad.2024.103809 NURBS Splatting 19 Supplementary Materials S1 Code and Data A vailability Code will be made available upon publication athttps://github.com/AnicoderAndy/nurbs-splattin...

    work page doi:10.1016/j.cad.2024.103809 2025