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Differences in canopy architecture play a role in determining both the light and water use efficiency. Canopy architecture is determined by several component traits, including leaf length, width, number, angle, and phyllotaxy. Phyllotaxy may be among the most difficult of the leaf canopy traits to measure accurately across large numbers of individual plants. As a result, in simulations of the leaf canopies of grain crops such as maize and sorghum, this trait is frequently approximated as alternating 180 angles between sequential leaves. We explore the feasibility of extracting direct measurements of the phyllotaxy of sequential leaves from 3D reconstructions of individual sorghum plants generated from 2D calibrated images and test the assumption of consistently alternating phyllotaxy across a diverse set of sorghum genotypes. Using a voxel-carving-based approach, we generate 3D reconstructions from multiple calibrated 2D images of 366 sorghum plants representing 236 sorghum genotypes from the sorghum association panel. The correlation between automated and manual measurements of phyllotaxy is only modestly lower than the correlation between manual measurements of phyllotaxy generated by two different individuals. Automated phyllotaxy measurements exhibited a repeatability of R2 ¼ 0.41 across imaging timepoints separated by a period of two days. A resampling based genome wide association study (GWAS) identified several putative genetic associations with lower-canopy phyllotaxy in sorghum. This study demonstrates the potential of 3D reconstruction to enable both quantitative genetic investigation and breeding for phyllotaxy in sorghum and other grain crops with similar lant architectures. 

Procedural modeling has produced amazing results, yet fundamental issues such as controllability and limited user guidance persist. We introduce a novel procedural system called PICO (Procedural Iterative Constrained Optimizer) using PICO-Graph, a procedural model designed with optimization in mind. PICO enables the exploration of generative designs by combining user and environmental constraints into a single framework and using optimization without the need to write procedural rules. The PICO-Graph is a data-flow procedural model consisting of a set of geometry-generating operation nodes. The forward generation is initiated by sending geometric objects from initial nodes. These objects travel through the graph, triggering generation of more objects along the way. We combine the PICO-Graph with evolutionary optimization that allows for exploration of the generated models and the generation of variants. The user defines the geometry-generating operations and the set of constraints; e.g, whether an existing object should be supported by the generated model, whether symmetries exist, etc. PICO then generates geometric models that fulfill the constraints through optimization, allowing interactive user control of constraints. We show PICO on a variety of examples, including generation of procedural chairs, generation of support structures for 3D printing, or generation of procedural terrains matching a given input. 

We introduce Dendry, a procedural function that generates dendritic patterns and is locally computable. The function is controlled by parameters such as the level of branching, the degree of local smoothing, random seeding and local disturbance parameters, and the range of the branching angles. It is also controlled by a global control function that defines the overall shape and can be used, for example, to initialize local minima. The algorithm returns the distance to a tree structure which is implicitly constructed on the fly, while requiring a small memory footprint. The evaluation can be performed in parallel for multiple points and scales linearly with the number of cores. We demonstrate an application of our model to the generation of terrain heighfields with consistent river networks. A quad core implementation of our algorithm takes about ten seconds for a 512 × 512 resolution grid on the CPU. 

Abstract Procedural modeling allows for an automatic generation of large amounts of similar assets, but there is limited control over the generated output. We address this problem by introducing Automatic Differentiable Procedural Modeling (ADPM). The forward procedural model generates a final editable model. The user modifies the output interactively, and the modifications are transferred back to the procedural model as its parameters by solving an inverse procedural modeling problem. We present an auto‐differentiable representation of the procedural model that significantly accelerates optimization. In ADPM the procedural model is always available, all changes are non‐destructive, and the user can interactively model the 3D object while keeping the procedural representation. ADPM provides the user with precise control over the resulting model comparable to non‐procedural interactive modeling. ADPM is node‐based, and it generates hierarchical 3D scene geometry converted to a differentiable computational graph. Our formulation focuses on the differentiability of high‐level primitives and bounding volumes of components of the procedural model rather than the detailed mesh geometry. Although this high‐level formulation limits the expressiveness of user edits, it allows for efficient derivative computation and enables interactivity. We designed a new optimizer to solve for inverse procedural modeling. It can detect that an edit is under‐determined and has degrees of freedom. Leveraging cheap derivative evaluation, it can explore the region of optimality of edits and suggest various configurations, all of which achieve the requested edit differently. We show our system's efficiency on several examples, and we validate it by a user study.