CrossShade:
Shading Concept Sketches Using
Cross-section Curves
Presenter: Feilong Yan

Introduction
Sketch
Shaded Sketch:
Production drawing

Introduction
• Manually shade with painting tools
• Convert sketch to complete 3D Model
Sketch
Manually shading

Introduction
• A natural question is “Is there a better way ?”
• Fast & reusable

This Paper
• This paper facilitates the creation of 3Dlooking shaded production drawing from sketches by the normal field estimated from cross section curves.
Sketch
Normal field
Production drawing

Main Work & Contribution
• 1. An explicit mathematical formulation of the relationship between sketched cross-section curves and the 3D geometry they aim to convey

Main Work & Contribution
• 2. An algorithm for extracting a normal field from cross-section curve networks based on the formulation above.

Cross Section & Cross Hair

Formulation
1. Orthogonal Cross-Hair Planes:
Perception studies indicate that designer consistently use orthogonal planes for intersecting cross-sections.

Formulation
2. Cross-Sections as Curvature Lines:
Perception studies indicate that observers interpret intersecting curves as aligned with the principal lines of curvature.

Formulation
3. Cross-sections as Local Geodesics:
Human perceive intersecting cross-section curves as geodesics
4. Minimal Foreshortening :
When drawing a shape, designers favor informative viewpoints that convey most visible surface with minimal foreshortening
5. Orientation:

Geometry Estimation
• Cross-Section Plane Estimation :
Use energy function constrained by 5 Formulations at the cross hair to estimate the support plane of cross-section curves
• Normal Propagation: curve normal estimation -> patch construction-> Coons interpolation

Cross-Section Plane Estimation
Assumption : Orthographic projection
Orthogonality:
 
 
 n i
 n j
 t ij
 t ji

 

( 1 )
( 2 )
Local Geodesics &Minimal Foreshorening: min n i
 ij
( t ji
 n i
2  t ji
 n i
Inherent Constrained:
2
)

( t ij z
)
2 
( t z ji
)
2 t ij
 n i

0 ( 4 )
( 3 )
At each cross-hair, the intersecting 3D curves share the same depth z: x
 n i
 c i

0 , x
 n j
 c j

0 ( 5 )

Normal Propagation
• Propagate the normals of the cross-hairs along the cross-section curves
• Interpolate all the sketch

Result

Result

Result

Not a Conclusion
• While the automatic shading quality can never match the expressiveness of manual artwork, the result are aspired , and can express the major features in the production drawing.
Sketch Manually shading
Automatic shading