Pushkar P. Joshi

Repoussé: automatic inflation of 2D artwork

We describe a new system for the interactive enhancement of 2D art with 3D geometry. Repoussé creates a 3D shape by inflating the surface that interpolates the input curves. By using the mean curvature stored at boundary vertices as a degree of freedom, we are able to control the inflated surface intuitively and efficiently using a single linear system. Repoussé handles both smooth and sharp position constraints. Position constraint vertices can also have curvature constraints for controlling the inflation of the local surface. We show the applications of our system in font design, stroke design, photo enhancement and freeform 3D shape design.

Energy Minimizers for Curvature-Based Surface Functionals

We compare curvature-based surface functionals by comparing the aesthetic properties of their minimizers. We introduce an enhancement to the original inline curvature variation functional. This new functional also considers the mixed cross terms of the normal curvature derivative and is a more complete formulation of a curvature variation functional. To give designers an intuitive feel for the preferred shapes attained by these different functionals, we present a catalog of the minimum energy shapes for various symmetrical, unconstrained input surfaces of different genera.

Surface Patches from Unorganized Space Curves

Recent 3D sketch tools produce networks of three‐space curves that suggest the contours of shapes. The shapes may be non‐manifold, closed three‐dimensional, open two‐dimensional, or mixed. We describe a system that automatically generates intuitively appealing piecewise‐smooth surfaces from such a curve network, and an intelligent user interface for modifying the automatically chosen surface patches. Both the automatic and the semi‐automatic parts of the system use a linear algebra representation of the set of surface patches to track the topology. On complicated inputs from ILoveSketch [ BBS08 ], our system allows the user to build the desired surface with just a few mouse‐clicks.

A Linear Variational System for Modelling From Curves

We present a linear system for modelling 3D surfaces from curves. Our system offers better performance, stability and precision in control than previous non‐linear systems. By exploring the direct relationship between a standard higher‐order Laplacian editing framework and Hermite spline curves, we introduce a new form of Cauchy constraint that makes our system easy to both implement and control. We introduce novel workflows that simplify the construction of 3D models from sketches. We show how to convert existing 3D meshes into our curve‐based representation for subsequent editing and modelling, allowing our technique to be applied to a wide range of existing 3D content.

Surface patches from unorganized space curves

Recent 3D sketch tools produce networks of three-space curves that suggest the contours of shapes. The shapes may be non-manifold, closed three-dimensional, open two-dimensional, or mixed. Our video demonstrates a system that automatically generates intuitively appealing, piecewise-smooth surface patches from such a curve network, and an intelligent user interface for modifying the automatically chosen surface patches. Both parts of the system use a linear algebra representation of the set of surface patches to track the topology.

Surface patches for 3D sketching

3D sketching is an appealing approach for creating concept shapes in the early stages of design. While curve networks alone can convey shape, surfacing the network can dramatically help with visualization and interaction. Unfortunately, surfacing a curve network is an inherently ambiguous problem, and even if the correct surface patches are identified, they can have an arbitrarily complex 3D geometry, making it challenging to produce a reasonable tessellation. In this paper we address the problem of creating light-weight surface tessellations on the fly. Our approach is to identify potential patches in the curve network, and then break complicated patches into simpler ones which can be tessellated using any simple algorithm. Our surfacing approach relies on the observation that breaking a complicated patch into a set of nearly planar ones with small total area seems to create a simple, natural-looking surfaces. We demonstrate our approach on curve networks generated by two different 3D sketching systems.

Efficient Non-linear Optimization via Multi-scale Gradient Filtering

We present a method for accelerating the convergence of continuous non‐linear shape optimization algorithms. We start with a general method for constructing gradient vector fields on a manifold, and we analyse this method from a signal processing viewpoint. This analysis reveals that we can construct various filters using the Laplace–Beltrami operator of the shape that can effectively separate the components of the gradient at different scales. We use this idea to adaptively change the scale of features being optimized to arrive at a solution that is optimal across multiple scales. This is in contrast to traditional descent‐based methods, for which the rate of convergence often stalls early once the high frequency components have been optimized. We demonstrate how our method can be easily integrated into existing non‐linear optimization frameworks such as gradient descent, Broyden–Fletcher–Goldfarb–Shanno (BFGS) and the non‐linear conjugate gradient method. We show significant performance improvement for shape optimization in variational shape modelling and parameterization, and we also demonstrate the use of our method for efficient physical simulation.

Graphics programming for the web

With HTML5 and ever-improving browser performance, the web has emerged as an ideal platform for showcasing graphics applications. Several graphics applications that were once too slow to be written in anything but native code may now be fast enough to run as web apps. This course for developers who want to develop graphics applications for the web introduces the concepts of core web programming and the dominant graphics technologies that are supported by most modern browsers. It begins with a brief primer on general-purpose web programming (HTML parsing, CSS, and DOM- and render-tree construction), how Javascript can be used to generate dynamic web content, and how to improve performance and accelerate development time. The bulk of this course describes the web technologies specific to graphics: CSS3: transitions, animations, 3D transforms and the new CSS-shaders HTML5 Canvas 2D: path API, compositing, image editing, and animation SVG: overview of API, how its different from HTML5 Canvas 2D WebGL: the key necessary steps, relation to OpenGL, performance hints WebCL: the formal specifications, whats implemented and whats to come For each topic, the course provides a significant number of code examples that illustrate the relevant graphics capabilities. Attendees are welcome to copy and paste our code snippets and execute them inside any modern web browser.

An intuitive explanation of third-order surface behavior

We present a novel parameterization-independent exposition of the third-order geometric behavior of a surface point. Unlike existing algebraic expositions, our work produces an intuitive explanation of third-order shape, analogous to the principal curvatures and directions that describe second-order shape. We extract four parameters that provide a quick and concise understanding of the third-order surface behavior at any given point. Our shape parameters are useful for easily characterizing different third-order surface shapes without having to use tensor algebra. Our approach generalizes to higher orders, allowing us to extract similarly intuitive parameters that fully describe fourth- and higher-order surface behavior.

Curve-Based Shape Modeling a Tutorial

This tutorial provides a starting point for curve-based modeling. It introduces three rough categories of curve-based-modeling methods: extruding 2D shapes, inflating 2D shapes, and drawing 3D curves. This tutorial introduces representative methods that yield positive results while also exposing several issues related to curve-based modeling.