2. Now days, sampled 3D models become more widespread in many fields and applications. It is often necessary to have a credible 2D model that emphasizes all visually relevant characters of the original object.

3. There are many common methods to capture a 3D object in 2D world focusing on different aspects of line drawing:

4. Definition: Points at which the normal (N) is perpendicular to the viewing direction (V). Occluding Contours Gives minimal information about the inward.

5. Definition: These are lines where a contour would appear with a minimal change of the viewing direction. Suggestive Contours [DeCarlo et al. 2004]

6. Definition: Ridges are points where curvature assumes local maxima. Valleys - local minima. Ridges and Valleys [Ohtake at al 2004] Curvature Amount of change in the normal, as we move in a specific direction on the object

7. Apparent Ridges [Tilke Judd 2007] Including viewing projection with curvature, defines the view- dependent curvature. These are points at which the view-dependent curvature attains a local maximum in the principal direction. Generates contours, and therefore can stand alone.

8. we project them on the object View- dependent curvature Given a specific point and direction in the view screen, and measure the change in the normal on the object. in regards to a small displacement on the screen,

9. Techniques innovation Presenting an image in a more artistic, human-like vision. Capturing essential visual properties and producing a non-photorealistic rendering of the image. Generating lines that are based on visual perception.

10. Trimming - both minima and maxima cases captured by zero crossing, for apparent ridges we eliminate the minima Estimate the view-dependent curvature derivative D t1 Locating zero crossings – determine inside which faces to draw a line Apparent Ridges Algorithm For each vertex on the mesh, find view-dependent curvature direction t1 Define a consistent t1 field, in the direction of the positive derivative Thresholding – draw lines that are only over certain value. Find two triangles that contain t1 and –t1 Intersection points w and w’ estimate the curvature there D t1 is the average Find two neighbor vertexes. If t1 fields co direct – there exists a zero crossing. Right – maxima Left - minima

11. We’ve implemented the Apparent Ridges algorithm for line drawing on meshes. Our implementation was much based on geometric and differential calculations. We’ve added our code to version 1.3 of rtsc. For more information look at our project book!

13. Threshold The Apparent Ridges technique finds all local extrema. However, we only care to remain with the meaningful lines.  keeping only the lines above a given threshold.

14. Comparison to Contours Contours provide limited information. Apparent Ridges images obtained without additional contour calculation.

15. Comparison to Ridges & Valleys Mathematically, ridges and apparent ridges are quite related. The Apparent Ridges method differs from the Ridges method by adding view-dependency. The Apparent Ridges lines offset from original ridges towards the contours.

16. At front facing parts of the model the methods do same. On parts that turn away from the viewer, they differ.

17. In our opinion, towards the contour the Apparent Ridges drawing is much more correct and points out the 3D effect. In zoomed in view Apparent Ridges looks more realistic, but the total image doesn't feel right.

18. Ridges and Valleys often provide a boxy looking object. While Apparent Ridges technique provides smoother lines. Difference noticeable around the nose and mouth.

19. The statues stand ornament is better illustrated by the Ridge and Valley technique. The figure itself seems more natural and feminine with the Apparent Ridges technique.

20. Comparison to Suggestive Contours In our opinion, the Suggestive Contours capture better the pattern of the Golf Ball. It is hard to compare Suggestive Contours to the Apparent Ridges because they are fundamentally different lines.

21. In convex regions of an object Suggestive Contours some times miss important features. In the Suggestive Contours image the ridge-like feature of the cube is missed whereas Apparent Ridges locate it properly.

22. The Suggestive Contours lines at the lips, nose, and chin area fit better the object. So is the stand of the statue. The Apparent Ridges image is not so good.

23. Conclusions Apparent Ridges: Generates contours, what makes the technique independent. Different models may point out lines that look better for one method or another. Often gave smoother results. Shows similarity to Ridges and Valleys technique. Differs from the Suggestive Contour technique.

24. Summery In this project we got exposed to 3D object analysis and terms. We’ve implemented the Apparent Ridges algorithm for line drawing. The comparison we made to other methods is subjective. Mostly, the view dependency addition resulted in smoother images with artistic aspect. We get outcome with 2D lines similar to the model, that describe it well and pleasant to view.