sketch-based modeling zhinan xu and mengyi zhu. motivation by providing the conversion between 2d...
TRANSCRIPT
MOTIVATION
By providing the conversion between 2D sketch and 3D model, the
designer will be able to quickly grasp the 3D properties of their sketch
and use it as initial model for the future modeling process
SEMANTIC CLASSIFICATION
By clicking the curve,
the user classify the
curve as feature curve
or silhouette curve
CURVE MATCHING
There are several definitions of curve distances.
𝑑𝑖𝑠 (𝑝 ,𝑞 )=∑𝑖=0
𝑛
min{ 𝑗=0…𝑚 }
𝑑𝑖𝑠 (𝑝𝑖 ,𝑞 𝑗 )
𝑛
Definition 1
Definition 2
CURVE MATCHING
Using the Hungarian method, we need to build the cost matrix and
process it by subtraction and optimal test, which will at most cost
Instead of finding the optimal combination(matching), we find one
“desired” combination by a greed algorithm. After constructing the
cost matrix, we scan the matrix to find the pair with minimum cost
and view this pair as a match. We continue this process until all
primitive curves are matched.
PRIMITIVES FITTINGS
Recall that we have vectorized points of the sketch and marked the feature curves.
At this step, we will try to fit virtual primitives to the sketch curves to draw 3D models.
PRIMITIVE FITTINGS
So far, our project supports fitting primitives of Sphere, Cylinder, Cones.
User will drag the primitives to match the sketch and while dragging, a run-time optimization step will help to determine the actual shape and placement of the 3D Model.
OPTIMIZATION
We use Augmented Lagragian Method to find a local maximum solution for the primitives parameters.
We make the use of the Objection Function used by A. Shtof et. al. for each primitives.
OPTIMIZATION --ALM
Better than penalty method
• Faster• Convert from CP to NCP
In order to find the local maximum solution of the NCP, we choose to implement the linear BFGS.
• Fast• Require knowledge of derivatives
PROBLEMS
Since it is an application with user interactions, performance is the most concern. We gave up a lot of accuracy to boost up the speed
However, the objective function for cylinder and cone doesn’t work well.
• Requires about 70 iterations• Some absurd parameters yield to smaller objective value
FUTURE WORK
A global optimization that consider relationship between objects (co-center, con-linear, normal and etc.)
A fix of the cylinder and cone objective function so it can give us satisfied result
An automatic vectorization process that allow us to load images and do snapping