HistCAD: Constraint-Aware Parametric CAD Histories for Evaluating Editability

Xintong Dong; Chuanyang Li; Peng Zheng; Chuqi Han; Jiaxin Jing; Hailong Shen; Yanzhi Song; Zhouwang Yang

cs.GRDec 8, 2025

HistCAD: Constraint-Aware Parametric CAD Histories for Evaluating Editability

Authors: Xintong Dong, Chuanyang Li, Peng Zheng, Chuqi Han, Jiaxin Jing, Hailong Shen, Yanzhi Song, Zhouwang Yang

Organizations: University of Science and Technology of China, Hefei, Anhui, P. R. China

Abstract

Sketch constraints specify geometric conditions for constructing and modifying parametric CAD models. We study whether predicted constraints allow a given history to reproduce the required initial model and support prescribed dimensional edits. We introduce HistCAD, an executable representation and dataset whose Academic and Industrial collections contain 180,495 parametric construction histories with entity-referenced sketch constraints and retained feature operations. Predictors receive these histories with the geometry and feature definitions retained and explicit sketch constraints removed. They generate constraints for every sketch without seeing the edit request. The benchmark compares models built with alternative constraint sets for the same history under the same dimensional edit. An edit succeeds when the model reproduces the required initial geometry, reaches the target value, preserves specified relations and unedited dimensions in the target sketch, and rebuilds through the complete history. A predictor trained on both collections and supplied with descriptions of the input histories achieves overall edit success of 52.4% on Academic and 29.0% on Industrial. Models retaining only endpoint-connectivity constraints in the target sketch and the history's constraints elsewhere can reach the target and rebuild while failing preservation. For all-sketch predictions, we retain the target-sketch prediction and restore the history's constraints in other sketches. More models then reproduce the required initial geometry, and some of these newly matched models complete the edit. HistCAD connects constraint learning to the construction and revision of parametric CAD models.

Figures & tables

Figure 1: HistCAD geometry examples (left) and an illustrative dimensional edit (right). In the illustrated sketch, Full retains all constraints, whereas Connectivity retains only profile-connectivity constraints. Both CAD models start from the same geometry, reach the target length, and rebuild successfully, but only the Full variant preserves the specified perpendicularity

L_{1}\perp L_{2}

Collection	Histories	Sketch constraints	Mean steps	Median steps	95th pct. steps	Distinct op. families
DeepCAD	153,534	2,755,327	1.47	1	3	1
Fusion 360	8,609	155,603	2.23	2	6	1
Industrial	18,352	565,984	6.23	3	19	5

Table 1: HistCAD collection sizes and history lengths. Constraint counts use the normalized entries and retain duplicate instances. Operation families are counted per collection. 95th pct. denotes the 95th percentile.

Figure 2: Edit evaluation from initial-model reproduction to dimensional modification. ER is the fraction of assigned tasks whose models pass pre-edit matching, attain the target, and rebuild validly ( $T=V=1$ ). OES additionally requires preservation of every specified relation and unedited dimension ( $P=1$ ).

		Academic (500 tasks)				Industrial (500 tasks)
Training	Condition	$M_{\mathrm{pre}}$	ER	Pres.	OES	$M_{\mathrm{pre}}$	ER	Pres.	OES
Academic only	History only	50.8	44.4	87.8	39.0	25.8	20.4	70.6	14.4
Academic only	Same-history description	59.8	55.8	91.8	51.2	28.2	24.6	80.5	19.8
Academic only	Shuffled description	26.6	24.8	79.8	19.8	15.6	13.4	71.6	9.6
Joint	History only	52.6	45.8	88.2	40.4	48.8	29.2	76.0	22.2
Joint	Same-history description	61.8	57.6	91.0	52.4	51.8	34.2	84.8	29.0

Table 2: All-sketch prediction outcomes (%). Joint denotes Academic–Industrial training. Maxima are bold for

M_{\mathrm{pre}}

, ER, and OES. The reachable edits included in Pres. can differ between conditions.

Task set	ER	Pres.	OES	ER	Pres.	OES	$\boldsymbol{\Delta}$ OES [95% CI]
	Full			Connectivity
Academic	99.6	100.0	99.6	100.0	53.0	53.0	46.6 [42.4, 50.6]
Industrial	79.2	100.0	79.2	82.4	44.4	36.6	42.6 [35.8, 49.6]

Table 3: Controlled edit outcomes (%). Both variants have

M_{\mathrm{pre}}=100\%

by task selection. Full’s 100% Pres. follows from the target-sketch feasibility criterion.

\Delta\mathrm{OES}

denotes Full minus Connectivity in percentage points, with 95% paired-bootstrap CIs.

Task set	Training	$M_{\mathrm{pre}}$	ER	Pres.	OES
Academic	Academic only	59.8 $\rightarrow$ 74.8	55.8 $\rightarrow$ 68.6	91.8 $\rightarrow$ 92.1	51.2 $\rightarrow$ 63.2
Academic	Joint	61.8 $\rightarrow$ 75.8	57.6 $\rightarrow$ 69.2	91.0 $\rightarrow$ 91.6	52.4 $\rightarrow$ 63.4
Industrial	Academic only	28.2 $\rightarrow$ 39.8	24.6 $\rightarrow$ 35.0	80.5 $\rightarrow$ 79.4	19.8 $\rightarrow$ 27.8
Industrial	Joint	51.8 $\rightarrow$ 68.6	34.2 $\rightarrow$ 48.4	84.8 $\rightarrow$ 84.7	29.0 $\rightarrow$ 41.0

Table 4: Edit outcomes before and after restoring the history’s constraints outside the target sketch (same-history descriptions; rates in %). Arrows denote all-sketch prediction

\rightarrow

non-target restoration. OES uses all assigned tasks. Restoration adds reachable edits, so Pres. uses different subsets before and after restoration.

Task set	Training	$\|H\|$	Pre-edit failure	Reachability failure	Preservation failure	Success
Academic	Academic only	282	52	10	15	205
Academic	Joint	275	49	11	13	202
Industrial	Academic only	83	13	1	14	55
Industrial	Joint	253	71	48	15	119

Table 5: Edit outcomes for predictions with history-level F1

\geq 0.8

, using same-history descriptions.

|H|

is the subgroup size. Membership can differ between predictors. Counts are mutually exclusive and sum to

|H|

. Reachability failure means passing initial matching but failing target attainment or valid rebuilding. Preservation failure means

P=0

for a reachable edit.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Component	Stored content and execution role
Coordinate system	Euler angles and a translation vector specify the pose of the local sketch plane in model coordinates.
Sketch primitives	Entity identifiers and line, circle, arc, ellipse, elliptical-arc, or NURBS parameters specify the stored sketch geometry.
Sketch constraints	Entries are grouped by type. For example, Length: [[line_1, 20.0]] assigns a length to a line, while Perpendicular: [[line_1, line_2]] makes the two lines perpendicular.
Feature operation	Feature fields specify the operation family and its parameters, including extrusion extents, a revolution axis and angles, and helical pitch and turns. NewBody, Join, Cut, and Intersect specify body interaction. Fillets and chamfers specify edge references and size parameters.
Step order	The sequence determines which body geometry and references are available when each operation executes.

Appendix

Table 6: HistCAD history components used for constraint-aware replay and feature execution.

Primitive	Identifier prefix	Geometric fields
Line	line_	start , end
Circle	circle_	center , radius ; optional taper
Circular arc	arc_	start , middle , end
Ellipse	ellipse_	center , major , minor , angle
Elliptical arc	elliptical_arc_	start , end , major , minor , angle , large_arc , sweep
NURBS	nurbs_	degree , periodic , controls ; weights and knots subject to the conditions below

Appendix

Table 7: Primitive fields in the common HistCAD format. A point is a two-element coordinate array in the local sketch frame. Ellipse semi-axis lengths satisfy major

\geq

minor

>0

JSON key	Single-entry form	Meaning and argument restrictions
Coincident	[p1, p2]	Two points coincide. Both operands are point references.
Concentric	[c1, c2]	Two center-bearing curves share a center.
Equal	[e1, e2]	Compatible entities have equal corresponding sizes: line pairs, round-curve pairs, ellipse pairs, or elliptical-arc pairs.
Fix	e or p	An entity or point is fixed.
Horizontal	l or [p1, p2]	A line is horizontal or two points share a $y$ coordinate.
Vertical	l or [p1, p2]	A line is vertical or two points share an $x$ coordinate.

Appendix

Table 8: Canonical constraint signatures. Each entry is stored in the array under its type key. Referenced entities and points belong to the same sketch.

Figure 3: Hierarchical and flat representations of the same selected sketch region. The hierarchical form stores face–loop membership, whereas HistCAD stores normalized boundary primitives. For the known face selection in the lower panels, shared interior boundary segments cancel after splitting into atomic edges, leaving the exterior and hole boundaries.

Figure 4: Example final geometries from the DeepCAD, Fusion 360 , and Industrial collections.

Panel A: Construction-history length
Collection	Histories	Mean	Median	95th pct.
DeepCAD	153,534	1.47	1	3
Fusion 360	8,609	2.23	2	6
Industrial	18,352	6.23	3	19

Appendix

Table 9: Structural coverage and constraint counts. A: construction steps per history, using nearest-rank percentiles. A sketch and its feature may share a step. B: Industrial histories can contain multiple operation families. C: 565,984 Industrial constraint instances in normalized histories, with duplicate multiplicity retained.

Quantity class	Equivalent dimension forms	Target attachment	Addition form
Curve size	Radius or Diameter on the same circle or arc	curve identifier	Radius
Line size	Length on a line; or unsigned MINIMUM Distance between its own endpoints	line identifier	Length
Other distance	Directional, point–line, cross-entity, and other Distance constraints	canonical entity or point references plus direction and half-space attributes	canonical Distance form

Appendix

Table 10: Equivalent dimensions used to construct tasks and locate their targets.

Comparison	Quantity	Acceptance
Solved-sketch position/length	Corresponding parameter residual divided by $s_{k}$	$\leq 10^{-6}$
Solved-sketch orientation	Unoriented ellipse-axis angular residual	$\leq 10^{-6}$ rad
Primitive identity	Corresponding identifiers and primitive kinds	Exact
Body count	Number of final bodies	Equal
Paired-body bounding box	Maximum corresponding-corner distance divided by $s_{b}$	$\leq 10^{-6}$
Paired-body volume	Relative-volume residual	$\leq 10^{-6}$

Appendix

Table 11: Pre-edit geometry matching. The body residual tolerances apply to every pair in the minimum-cost assignment. Topological counts are used only to select the body pairs.

Constraint type	Geometric quantity	Tolerance
Coincident	Maximum referenced-point separation	0.01 mm
Concentric	Maximum center separation	0.01 mm
Midpoint	Point-to-segment-midpoint separation	0.01 mm
Parallel / Perpendicular	Line-direction deviation from $0^{\circ}/180^{\circ}$ or $90^{\circ}$	$0.5^{\circ}$
Angle	Circular angular difference	$0.5^{\circ}$
Horizontal / Vertical	Line-to-axis angle; absolute $y$ - or $x$ -coordinate difference between the two referenced points	$0.1^{\circ}$ for lines; $\epsilon_{\ell}$ for points

Appendix

Table 12: Quantities and tolerances for target attainment and preservation.

Setting	Value
Base model	Qwen3-8B
Chat format and thinking mode	Qwen3 chat format; training and inference configured with thinking disabled
LoRA rank / alpha / dropout	256 / 128 / 0.05
LoRA modules	query/value projections
Optimizer	AdamW
Learning-rate schedule	Peak $5\times 10^{-5}$ , 1% warmup, cosine decay to 10% of peak

Appendix

Table 13: Training and inference settings.

Academic prediction test set ( $n=6{,}382$ )
		All types	Non-Coincident
Training	Prediction condition	Micro-F1	P	R	F1	Available, $n$ (%)
Academic only	History only	67.40	40.88	53.73	46.43	6,300 (98.72)
Academic only	Same-history description	72.98	51.57	60.88	55.84	6,299 (98.70)
Academic only	Shuffled description	61.46	33.20	41.35	36.83	6,078 (95.24)
Joint	History only	68.31	42.34	54.30	47.58	6,288 (98.53)

Appendix

Table 14: Constraint scores and availability on the full prediction test sets (%). Scores pool TP, FP, and FN over each test set; Non-Coincident scores exclude Coincident constraints. P and R denote precision and recall. Available

n

(%) counts complete, parseable, aligned outputs. Its denominator is all 6,382 Academic or 915 Industrial inputs, including those for which generation was skipped.

A. Joint minus Academic-only training
Task set	Prediction condition	$\Delta M_{\mathrm{pre}}$ [95% CI]	$\Delta\mathrm{OES}$ [95% CI]
Academic	History only	$+1.80$ [-1.00, 4.80]	$+1.40$ [-1.40, 4.20]
Academic	Same-history description	$+2.00$ [-0.80, 5.00]	$+1.20$ [-1.60, 4.00]
Academic	Shuffled description	$-1.00$ [-4.00, 1.80]	$+0.40$ [-2.20, 3.00]
Industrial	History only	$+23.00$ [12.96, 32.64]	$+7.80$ [1.88, 14.42]
Industrial	Same-history description	$+23.60$ [15.07, 32.40]	$+9.20$ [3.30, 15.90]

Appendix

Table 15: Paired differences in pre-edit matching and overall success, expressed in percentage points with 95% paired-bootstrap CIs. Each comparison uses the same 500 tasks per set. Panel headings specify subtraction order.

Task set	Training	Matched $m$	OES (%)	Pre-edit failure $\rightarrow$ success
Academic	Academic only	299 $\rightarrow$ 374	51.2 $\rightarrow$ 63.2	60
Academic	Joint	309 $\rightarrow$ 379	52.4 $\rightarrow$ 63.4	55
Industrial	Academic only	141 $\rightarrow$ 199	19.8 $\rightarrow$ 27.8	40
Industrial	Joint	259 $\rightarrow$ 343	29.0 $\rightarrow$ 41.0	60

Appendix

Table 16: Outcomes before and after restoring the history’s constraints outside the target sketch, using same-history descriptions and an unchanged target-sketch prediction. Both conditions use the complete construction history. Arrows show before-to-after restoration values. OES uses all 500 tasks in each set. The last column counts tasks changing from pre-edit failure to success.

Task set	Training	Input	Pre fail	Reach fail	Pres fail	Success
Academic	Academic only	History only	246	32	27	195
Academic	Academic only	Same-history	201	20	23	256
Academic	Academic only	Shuffled	367	9	25	99
Academic	Joint	History only	237	34	27	202
Academic	Joint	Same-history	191	21	26	262
Academic	Joint	Shuffled	372	10	17	101

Appendix

Table 17: Full-population outcome counts derived from Table 2 . Every row sums to 500. Pre fail: unavailable prediction or failed pre-edit replay or geometry matching; Reach fail: pre-edit matching passes but target attainment or valid rebuilding fails; Pres fail: reachable with

P=0

A. All tasks
Task set	Training	Prediction condition	$\rho$ [95% CI]	Failed tasks F1 $\geq 0.8$	Successful tasks F1 $\leq 0.2$
Academic	Academic only	History only	0.528 [0.455, 0.595]	76/215 (35.3)	0/12 (0.0)
Academic	Academic only	Same-history description	0.595 [0.533, 0.653]	77/282 (27.3)	0/14 (0.0)
Academic	Joint	History only	0.473 [0.394, 0.546]	79/218 (36.2)	0/12 (0.0)
Academic	Joint	Same-history description	0.605 [0.543, 0.661]	73/275 (26.5)	0/13 (0.0)
Industrial	Academic only	History only	0.416 [0.331, 0.501]	17/47 (36.2)	0/221 (0.0)

Appendix

Table 18: History-level F1 and edit success under all-sketch prediction. A uses all 500 tasks per set, including pre-edit failures. For each predictor, failure and success fractions use the numbers of tasks with prediction F1

\geq 0.8

and

\leq 0.2

, respectively, as denominators. B excludes unavailable predictions but retains those whose models fail pre-edit matching. Brackets give 95% bootstrap CIs.

A. Academic
Full / Connectivity	Success	Reachable; preservation failure	Not reachable
Success	264	234	0
Reachable; preservation failure	0	0	0
Not reachable	1	1	0
B. Industrial
Full / Connectivity	Success	Reachable; preservation failure	Not reachable

Appendix

Table 19: Paired Full–Connectivity outcomes on the complete controlled sets. Rows are Full outcomes and columns are Connectivity outcomes. Each panel contains 500 paired tasks from one collection. Row and column totals give the counts used for ER and OES. Both controls pass pre-edit matching. Preservation failures include unresolved references and failed measurements as well as measured geometric violations.

Figure 5: Failures before the prescribed edit. Initial is the reference. Full and Joint show successful edits. Academic-only* fails before the requested change is applied. The requests are (a) shortening the base of Industrial 01020012 (two chamfers and a fillet) and (b) widening a cut profile in Industrial 01022672 (three fillets). Extra predicted constraint groups prevent history construction in (a,b).

\times

marks these output errors. In (c), the request is to increase the distance from an arc center to an endpoint in Academic 01005050. During initial replay, Academic-only distorts the arc profiles and fails Boolean extrusion (partial model shown). The requests in (d,e) are to lengthen a sleeve-profile segment in Industrial 01027877 and enlarge the inner circle of Industrial 01016299, respectively. The solved Academic-only sketches already mismatch the reference in both cases. Models appear above target sketches. Dark solid lines show displayed geometry and light dashed lines show the initial reference.

Figure 6: Failures after pre-edit matching. Initial is the reference; all other columns show results of the same edit. Full and Joint succeed throughout. Under Academic-only, (a) the lower edge of Industrial 01016487 reaches its requested longer length, but a downstream cut misses the body; (b) the opening in Academic 00465180 reaches its requested larger size, but a perpendicular constraint is skipped and the sketch deforms. These two model panels show incomplete replays. In (c) Academic 01004348, reducing the distance across the lug leaves the hole off-center within the rounded top. In (d) Academic 00592341, extending a horizontal step edge also changes an unedited edge length. In (e) Industrial 01024010, a specified right angle is lost when one rectangle side is lengthened. The last three Academic-only results attain the target and rebuild validly, but fail preservation. Models appear above target sketches; dark solid lines show displayed geometry and light dashed lines show the initial reference. Plus signs mark the centers in (c).

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