Improving the Sketch-Based Interface - Forming Curves from Many Small Strokes

Authors:
Richard Pusch, Faramarz Samavati,
University of Calgary,

Ahmad Nasri,
American University of Beirut,

Brian Wyvill
University of Victoria

Summary:
There is a divide in interaction between user / pen & paper and user / touch interfaces while drawing. One important problem is the ability the correct the stroke in the paper by over drawing a long stroke with small strokes to make local corrections.

This paper proposes a new method to create a smooth stroke out of many small strokes.
First important step is to find the global ordering of the stroke. This is done by running a PCA over the starting points of the stroke. This process is made easier by dividing the strokes in to boxes and connecting them. The boxes obtained are sub - divided until they become simple. Condition for simple box - closeness of the strokes inside the box to the straight line (measured by ratio of eigenvalues) / box containing single line.

metric for dividing a box - a largely horizontal box will be divided into 2 horizontal halves rather than vertical divisions. A straight stroke / stroke with more points should be taken as dominant strokes in deciding the division of the box. In order to find the method of division, a metric is formed using weighted average of the angle between the x-axis and each stroke's primary eigenvector. This is weighted using the ratio of the eigen values. This metric is used to find which of the 3 following division will be made - vertical, horizontal or both.

Once the box is chosen, then the ordering of strokes is performed by projecting the strokes on the dominant eigen vector. for overlapping strokes, the overlap is substituted by a average curve.

Next step, the boxes are connected by finding the last point of the local ordering and finding the stroke which it belongs to and continue on that stroke.After this step, a b-spline curve is fit to the strokes.

Discussion:
It would be interesting to implement something like a fudge tool. Move over every point in base line, any line that falls with in a particular radius should be merged with the base stroke.

Sketch- and Constraint-based Design of B-spline Surfaces

Authors:
Paul Michalik, Dae Hyun Kim, Beat D. Bruderlin
Computer Graphics Group, Dept. of CS
Technical University of Ilmenau, Germany

Summary:
To join 2 splines- first the portion of the base curve relevant for merging is identified. Then merged with correction curve. A part to the left and right of base stroke is identified as the transition part, to give a gradual merging to the corrected curve.

Modes provided for 3D image editing:
1. Sweeping mode - mode to draw the initial set of curves
2. Skinning mode - to add curves to the already identified surfaces.
3. Sculpting mode
The sketch space. surface is showed using blue hatch lines. In the sculpting mode, each line drawn by the user leads to a constraint graph. each node is a constraint given by the user and the error calculated for the surface on the constraint. each node has weight associated with it which helps solve the over-constrained graphs.

Discussion:
the summary is not complete.. The lot of these mathematical modeling techniques expect the user to understand the maths behind it which might not be possible. This can affect the interaction between the user and the system considerably. A system that defines the method of user drawing constraints the user ability. "A good idea is to start with relatively simple surface, and let the system automatically introduce new DOFs at appropriate locations, if errors at the constraints exceed defined limits."