We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e., Gauss's equation and the Mainardi-Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles as the discrete second fundamental form. The resulting sparse linear system to solve for the immersion is derived from the convex optimization of a quadratic energy based on a lift from the immersion in the 3D Euclidean space to the 6D rigid motion space. This discrete representation and linear reconstruction can benefit a wide range of geometry processing tasks such as surface deformation and shape analysis. A rotation-invariant surface deformation through point and orientation constraints is demonstrated as well.

Based on a new spectral vector field analysis on triangle meshes, we construct a compact representation for near conformal mesh surface correspondences. Generalizing the functional map representation, our representation uses the map between the low‐frequency tangent vector fields induced by the correspondence. While our representation is as efficient, it is also capable of handling a more generic class of correspondence inference. We also formulate the vector field preservation constraints and regularization terms for correspondence inference, with function preservation treated as a special case. A number of important vector field–related constraints can be implicitly enforced in our representation, including the commutativity of the mapping with the usual gradient, curl, divergence operators or angle preservation under near conformal correspondence. For function transfer between shapes, the preservation of function values on landmarks can be strictly enforced through our gradient domain representation, enabling transfer across different topologies. With the vector field map representation, a novel class of constraints can be specified for the alignment of designed or computed vector field pairs. We demonstrate the advantages of the vector field map representation in tests on conformal datasets and near‐isometric datasets.

Production of h. orticultural crops by growers is becoming increasingly difficult as markets write detailed specifications for products both in time of delivery and quality factors such height and flower number. Such specifications require growers perform proper cultural procedures at the proper time. Environmental variation between and among seasons means proper cultural procedures will vary with every crop. All growers, especially those with little experience in a crop, benefit from information that assist in making proper cultural-procedure decisions. Decision-support tools based on environmental, chemical, or biological data can help provide such information. This presentation will describe examples of biological concepts associated with plant growth and developmental processes that especially lend themselves to decision-support. Types of decision-support tools developed from this information will be presented. For example, development of plants is highly temperature dependent. Relationships between temperature and development rate are often useful as they can be described by a linear relationship over a wide temperature range from the base temperature to near the optimum temperature. Degree-day decision-support tools can be developed from such information. Growth retardant chemicals are used widely in commercial production of flowering plants to meet height-control specifications. Simulation models incorporated into decision-support tools may be useful to maximize efficacy of applications as there is increasing pressure to minimize the use of growth retardants. Biological models relating plant morphological development to the environment, e.g., bud length and temperature to time to flower, can also be useful in creating decision-support tools for accurate crop timing.

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