Precise elevation design on an aerially reconstructed terrain can ensure an appropriate structural slope for good driving conditions and dovetail the design with real world. Traditional planners are used to drawing curves for 2D floor design, but there is no mechanism to design a 3D terrain based on editing the cross-section of selected 2D ground curves. Therefore, this work aims to bridge the gap between the intuitive 2D curve-based design practice and precise 3D terrain construction. Since floor planners generally refer to 2D cross-sections for elevations and are more familiar with curve manipulation instead of 3D mesh editing, this work proposes an elevation modeling tool based on editing the 2D cross-section of user-drawn ground-projected curves. The system is designed to align with intuitive 2D curve-based design practices by first letting users draw curves on the ground as 3D-constrained parametric curves. It constructs a ground-projected plane for 2D cross-sectional manipulation to achieve precise altitude control. The system diffuses the parametric elevations to their surroundings and constructs its height field by solving the corresponding differential equation. Finally, remeshing is applied to ensure patch boundaries precisely align with the constrained curves. Thus, our system can address the difficulty and complexity in precise elevation control and boundary alignment of brush-style, feature-based, and NURBS-based knot-tuning methods. Numerical experiments and a usability study of naive users and experts demonstrate our intuitiveness and effectiveness over state-of-the-art methods and verify our ability to mimic traditional 2D curve-based design practice.

Generative models based on deep neural networks often have a high-dimensional latent space, ranging sometimes to a few hundred dimensions or even higher, which typically makes them hard for a user to explore directly. We propose differential subspace search to allow efficient iterative user exploration in such a space, without relying on domain- or data-specific assumptions. We develop a general framework to extract low-dimensional subspaces based on a local differential analysis of the generative model, such that a small change in such a subspace would provide enough change in the resulting data. We do so by applying singular value decomposition to the Jacobian of the generative model and forming a subspace with the desired dimensionality spanned by a given number of singular vectors stochastically selected on the basis of their singular values, to maintain ergodicity. We use our framework to present 1D subspaces to the user via a 1D slider interface. Starting from an initial location, the user finds a new candidate in the presented 1D subspace, which is in turn updated at the new candidate location. This process is repeated until no further improvement can be made. Numerical simulations show that our method can better optimize synthetic black-box objective functions than the alternatives that we tested. Furthermore, we conducted a user study using complex generative models and the results show that our method enables more efficient exploration of high-dimensional latent spaces than the alternatives.