SKETCH-BASED MODELING ZHINAN XU AND MENGYI ZHU. MOTIVATION By providing the conversion between 2D sketch and 3D model, the designer will be able to quickly.

SKETCH-BASED MODELING

ZHINAN XU AND MENGYI ZHU

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

UI OVERVIEW

SKETCHINGAfter clicking “draw”

button, the user first

sketch on our

painter

SEMANTIC CLASSIFICATION

By clicking the curve,

the user classify the

curve as feature curve

or silhouette curve

CURVE MATCHING

Support translation, scaling and rotation

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 – OBJECTIVE FUNCTION

Sphere:

Cylinder:

Cone:

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