Trees are a ubiquitous part of virtual environments, but faithfully modeling trees is challenging because of their incredible diversity. Tree modeling methods face two key challenges, as users want to create trees that look realistic but retain control over key elements of their appearance, such as the shape of the tree crowns. Traditional tree modeling methods are geared to produce tree models that are both detailed and unique and are typically stored as high-triangle count meshes or skeletons plus radii. Storing and manipulating such traditional tree models comes with a significant memory cost. Recent approaches have proposed to use modular trees consisting of a finite set of branch modules, which are transformed (scaled, translated, and rotated) to jointly form realistic looking trees. Consequently, modular trees require orders of magnitude less memory than their traditional counterparts. However, existing methods for modeling modular trees focus on visual realism and provide only minimal mechanisms for artists to control the look and shape of the resulting trees. We propose a controllable method for modeling modular trees, enabling artists to define the tree’s overall crown shape while maintaining a plausible appearance using a small set of replicated branch modules. We formulate the computation of realistic modular trees that conform to a user-specified crown shape as a constrained mixed-variable optimization problem. We then compute the trees that satisfy these constraints using a method that grows trees one layer of branches at a time, maintaining realism throughout and promoting accurate approximation of the target crown shape. We extensively test our method on diverse crown shapes and compare against baselines, demonstrating its effectiveness.

Artist-drawn sketches only loosely conform to analytical models of perspective projection; the deviation of human-drawn perspective from analytical perspective models is persistent and well documented, but has yet to be algorithmically replicated. We encode this deviation between human and analytic perspectives as a continuous function in 3D space and develop a method to learn it. We seek deviation functions that (i) mimic artist deviation on our training data; (ii) generalize to other shapes; (iii) are consistent across different views of the same shape; and (iv) produce outputs that appear human-drawn. The natural data for learning this deviation is pairs of artist sketches of 3D shapes and best-matching analytical camera views of the same shapes. However, a core challenge in learning perspective deviation is the heterogeneity of human drawing choices, combined with relative data paucity (the datasets we rely on have only a few dozen training pairs). We sidestep this challenge by learning perspective deviation from an individual pair of an artist sketch of a 3D shape and the contours of the same shape rendered from a best-matching analytical camera view. We first match contours of the depicted shape to artist strokes, then learn a spatially continuous local perspective deviation function that modifies the camera perspective projecting the contours to their corresponding strokes. This function retains key geometric properties that artists strive to preserve when depicting 3D content, thus satisfying (i) and (iv) above. We generalize our method to alternative shapes and views (ii,iii) via a self-augmentation approach that algorithmically generates training data for nearby views, and enforces spatial smoothness and consistency across all views. We compare our results to potential alternatives, demonstrating the superiority of the proposed approach. Code and models will be released upon acceptance.

Compressed representations of 3D shapes that are compact, accurate, and can be processed efficiently directly in compressed form, are extremely useful for digital media applications. Recent approaches in this space focus on learned implicit or parametric representations. While implicits are well suited for tasks such as in-out queries, they lack natural 2D parameterization, complicating tasks such as texture or normal mapping. Conversely, parametric representations support the latter tasks but are ill-suited for occupancy queries. We propose a novel learned alternative to these approaches, based on intersections of localized explicit , or height-field , surfaces. Since explicits can be trivially expressed both implicitly and parametrically, NESI directly supports a wider range of processing operations than implicit alternatives, including occupancy queries and parametric access. We represent input shapes using a collection of differently oriented height-field bounded half-spaces combined using volumetric Boolean intersections. We first tightly bound each input using a pair of oppositely oriented height-fields, forming a Double Height-Field (DHF) Hull . We refine this hull by intersecting it with additional localized height-fields (HFs) that capture surface regions in its interior. We minimize the number of HFs necessary to accurately capture each input and compactly encode both the DHF hull and the local HFs as neural functions defined over subdomains of \(\mathbb {R}^2\) . This reduced dimensionality encoding delivers high-quality compact approximations. Given similar parameter count, or storage capacity, NESI significantly reduces approximation error compared to the state-of-the-art, especially at lower parameter counts.