The design of furniture consists of two major components: geometric modeling and physical validity of shapes. While advances in software for 3D modeling have made it easier for even inexperienced users to design shapes and thus make content creation easy, there is a disconnect between the geometric design and the physical functionality assessment. The typical workflow for a designer is to create a 3D model followed by validation using a physical simulator, and depending on the validation results, the designer re-iterates the whole process. This is tantamount to trial-and-error, making it a slow process, not to mention (a) the lack of any feedback to the designer specific to why the design failed and (b) the inherent limited exploration of novel shapes by encouraging designers to opt for standard geometric shapes only. While there have been previous work on suggestive modeling and interactive shape exploration, these works are limited in their feedback such as providing only a binary response about whether the design is valid or not, lack of informed exploration, etc. This paper proposes “a computational design framework for efficient and intuitive exploration” of physically valid furniture design shapes. In particular, the framework allows constrained modeling of nail-jointed furniture design of furniture using medium density fiberboard, and is constrained on 3 conditions: connectivity, durability, and stability. The paper describes the proposed method and the theoretical justifications in explicit detail, and we provide a brief summary of the key details here.
The proposed modeling interface contains
a modeling panel specialized for nail-jointed plank based design and
a suggestion panel offering suggestions if the design in the modeling panel is invalid.
The system continuously checks the validity of the design for geometric and physical requirements, i.e., connectivity, durability, and stability, and presents the analysis to the user during “mouse dragging”. The system also continuously highlights the type of invalid configuration: disconnected join, broken joint, or topple axis, as the user interacts with the interface. Additionally, if the design is invalid, the model provides 8 suggestions in the suggestion panel to resolve the error, and these suggestions allow “coordinated editing”, permitting the user to drag the highlighted arrows to control the multiple degrees of freedom so as to satisfy the constraints. As the user edits the design, first the geometric constraints are satisfied by checking for joint connectivity and ground contact, and suggesting discrete changes (by adjusting the lengths of the planks) if not. Next, the physical validity is evaluated by testing for durability and stability by checking for inequality constraints on the joint forces and the contact forces respectively, and if not, appropriate suggestions are presented. For measuring durability, the component planks used for furniture design are modeled as “assemblies of unbreakable rigid bodies”. A joint in the design is deemed durable if both the pulling force and the shear force at the joint are within “allowable threshold margins”, and this is repeated for all joints in the design. For measuring the stability, the authors carry out a sensitivity analysis with an assumption that the designed model is “casually placed” on the ground and is not bolted to the ground, essentially implying that friction is necessary to avoid sliding. The framework also provides the user with a guided exploration of the valid subspace of the configuration space. The authors note that in addition to the durability and the stability constraints, the connectivity constraints also provide geometrical restrictions in the form of joint constraints and contact constraints. Since a shape is considered valid only if it is durable and stable, the valid space tends to have a complex boundary in a high-dimensional space. The paper makes a few assumptions and approximations to easy the optimization:
the translation force is constant for small design changes but the bending force varies,
the shearing force is constant for small design changes, and
forces vary linearly w.r.t. design variations under local changes.
For the shape suggestions, instead of searching for all parts, the paper focuses on suggestions involving at most a fixed certain number of degrees of freedom per suggestion. Moreover, the model is able to provide both continuous and discrete shape suggestions, depending upon the type of invalid configuration. For evaluation, 2 chairs and 2 bookshelves with non-conventional designs were modeled, and it was shown that a trial-and-error approach to ensure physical validity of the designs was non-trivial, and that providing suggestions helped considerably. Furthermore, a user study was conducted amongst 9 graduate students who were novice designers, and one subgroup of 5 participants was asked to work with 3 systems in increasing order of design feedback provided during modeling with the third system being the one proposed in this paper, and the other subgroup of 4 participants with the same 3 systems but in the opposite order. For the first group, the users found it difficult to create realistic reproductions of their planned designs with the first 2 systems and they were successful with the third system. For the second group, even though the users had seen the design feedback before (they were using systems in decreasing order of feedback provided), they struggled to realize their planned designs with the two systems which did not provide continuous feedback.
This paper presents a computational framework for guided design and exploration of valid spaces for furniture. The presence of constant feedback in terms of highlighted invalid configurations and design suggestions helped improve the utility of the framework considerably. The paper is written very clearly with sufficient background information and illustrated examples to explain the concepts and the design choices, and is therefore easy to read and follow. A few potential shortcomings of the method:
the authors write that “the exact placement of the weight on the selected plank is not important”, but such a simplification would not hold true for large planks and for planks made of different materials,
the component planks are modeled as “unbreakable rigid bodies”, and this assumption may lead to undurable models when the design structure gets more complex, and
the forces involved are assumed to vary linearly w.r.t. the design variations, but incorporating higher order approximations may lead to more accurate design.