Growth tensor of plant organs

Hejnowicz, Z.; Romberger, J. A.

doi:10.1016/s0022-5193(84)80017-x

Cited by 72 publications

(95 citation statements)

References 6 publications

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“…Growth can be characterized by the growth tensor field [Hejnowicz and Romberger 1984], which specifies the magnitude of the expansion of infinitesimal surface regions in various directions, and may include a possible rotation of each region. The growth tensor is a generalization of the relative elementary rate of growth (RERG), which is defined as the rate at which an infinitesimal distance ∆s, measured in the direction of a line l at a point p of a growing object, increases over time.…”

Section: Mathematical Description Of Leaf Growthmentioning

confidence: 99%

Modeling and visualization of leaf venation patterns

Runions

Fuhrer

Lane

et al. 2005

ACM SIGGRAPH 2005 Papers

204

167

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We introduce a class of biologically−motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodes and auxin sources. In addition, a vein connection graph is maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree−like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research. Reference Modeling and visualization of leaf venation patterns AbstractWe introduce a class of biologically-motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodesandauxinsources.Inaddition,aveinconnectiongraphis maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree-like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research.

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Section: Mathematical Description Of Leaf Growthmentioning

confidence: 99%

Modeling and visualization of leaf venation patterns

Runions

Fuhrer

Lane

et al. 2005

ACM SIGGRAPH 2005 Papers

204

167

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“…1l). Inclined cell walls have been reported in LR primordia of radish [9] in which oblique divisions at early stages led to formation of cuneiform cells, and in Arabidopsis [6], in which such walls were interpreted as a manifestation of a change of the principal directions of growth (PDG) [10] within the de novo formed meristem.…”

Section: Resultsmentioning

confidence: 99%

Various scenarios of the cell pattern formation in Arabidopsis lateral root

2014

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During lateral root (LR) development a coordinate sequence of cell divisions, accompanied by a change of the organ form takes place. Both the order of anatomical events and morphological features may vary for individual primordia. At early stages of LR primordia development oblique division walls are inserted in cells that are symmetrically located on both sides of the axis of the developing LR primordium, and thereby allow for the protrusion of the LR. We hypothesize that both oblique cell wall insertion and continuous changes in primordium form could be a consequence of a local change in stress distribution in the region of the LR initiation.

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“…The relative elementary growth rate RERG l(ζ) is the rate at which an infinitesimal distance Δζ, measured in the direction of growth line at a point on growing silhouette, increases over time. RERG is mathematically defined as [Hejnowicz and Romberger 1984]:…”

Section: Leaf Type Modelingmentioning

confidence: 99%

“…In this paper we will character the growth by growth tensor field at X and Y and Z coordinates [Hejnowicz and Romberger 1984;Nebelsick et al 2001;E et al 2004]. The growth tensor allows full characterization of the rate of growth in length, area, and volume, as well as rates of angular change between elements, and of vorticity in the growing organ.…”

Section: Introductionmentioning

confidence: 99%

Procedural techniques for simulating the growth of plant leaves and adapting venation patterns

Alsweis

Deußen

2015

Proceedings of the 21st ACM Symposium on Virtual Reality Software and Technology

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This paper presents biologically-motivated a procedural method for the simulation of leaf contour growth and venation development. We use a mathematical model for simulating the growth of a plant leaf. Leaf tissue is regarded as a viscous, incompressible fluid whose 2D expansion is determined by a spatially varying growth rate. Visually realistic development is described by a growth function RERG that reacts to hormone (auxin) sources embedded in the leaf blade. The shape of the leaf is determined by a set of feature points within the leaf contour. The contour is extracted from photos by utilizing a Curvature Scale Space (CSS) Corner Detection Algorithm. Auxin transport is described by an initial auxin flux from an auxin source to an auxin sink that is gradually channelized into cells with high levels of highly polarized transporters. The leaf is presented as a triangulated double layer structure that consists of a Voronoi-Diagram that is discretised along the vein structures.

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Growth tensor of plant organs

Cited by 72 publications

References 6 publications

Modeling and visualization of leaf venation patterns

Modeling and visualization of leaf venation patterns

Various scenarios of the cell pattern formation in Arabidopsis lateral root

Procedural techniques for simulating the growth of plant leaves and adapting venation patterns

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