Paragraphs about Papers for CS680 for 3/5/97

Via a variety of different grammar elements, various different types of plants can be developed. For instance, racemes can be modeled. The grammars can produce combinations of basitonic or acrotonic plant structures and basipetal or acropteal flowering sequences, as desired; this is done by modeling signals. Delays can also be created using the grammars, so that different portions are developmentally different. The grammar can even count, and progress to use different production based upon that count. Equally important, the grammar can be made non-deterministic, so that one of several productions is randomly used. As mentioned in the paper, without this randomization, a picture of several plants would look highly artificial, because the plants would look too similar. With non-determinism and the same grammar, the plants will look naturally different, but close enough to belong to the same species.

Once the primordia are placed, each primordium is replaced by the desired organ. This creates the final picture, which has the mature organs and retains the spiral phyllotaxis which was generated using the primordia. As mentioned in the paper, one of the missing details is the interactions between the mature organs. Thus, this doesn't accurately create an image when the organs are compressed, or moving; it certainly doesn't cover the development of the plant. The processing power required by this method is apparently very low. The user can interactively create and modify the receptacle, primordia, and organs. This method seems like an excellent, practical tool for creating images including spiral phyllotaxis.

`Developmental Models of Herbaceous Plants for Computer Imagery Purposes" by Przemyslaw Prusinkiewica, Aristid Lindenmayer and James Hanan. Computer Graphics, Vol 22, Number4, August 1988.

This paper describes a method for creating realistic plant modesl. It covers both animation techniques and still images. The process used focused on two major asspects. First on making the plants look realistic and second and possiable more important on making the modeling process based as much as possible on the acctual processs plants go throught when they are growing.

A L-system formaliszm was used to model the plants. They used a number of varius terms to correlate the biological context and the computer graphics context. The concept of the rooted tree is extreamly inportant in this paper for they are dealing mainly with a particualr type of rooted tree called a Axial tree. In nature there are two aspect that control plant development the linege, genetic inforamtion is passed on, and the interactive, by which the cells of the plant communicatie. The L-system provide the representtion of the linege process by context-free productions and the interactive mechanisms are representsd bye the contxext senstive porductions. To draw out the gemetry the used a logo like turttle that would uses a series of commnads to get the final image.

The strenght of this paper is how they kept close to the process that they were simulating. This process is very close to the process that plants go through when they are created. They even introduce some statictical variitaiotn into the plant develompment to get various different types looks and shapes to the structures.

`A Collision-based Model of Spiral Phyllotaxis' by Deborah R. Fowler, Przemyslaw Prusinkiewicz and Johannes Battjes. Computer Graphics Vol:26, Number: 2 July 1992.

This paper discribes how to model the sprial pattersn that are often found in plants and in nature. It usess a prcess of minimizing collsion detction to accomplish this task. These spirals are often found in nature to have many interesting mathimatical regualrities. In observing natures packing method and duplicating it is how this process works. The primordia or protuding like structures that finaly become flowers or fruit are placed next to one another by using a angle of 137.5 degrees. Each of the primordia are place in this manner until they collied with one another. These primordia are modeled as spheres in the process described.

P. Prusinkiewicz, et. al., Developmental Models of Herbaceous Plants for Computer Imagery Purposes

This paper was motivated by the idea (long held in the biology community) that the final shape an organism takes depends heavily on the developmental processes it undergoes. Thus, Prusinkiewicz maintains, the best way to realistically render plants on a computer is not to simply draw an entire plant, but to "grow" the plant, rendering the most of developmental process as well as the finished product.

To do this, Prusinkiewicz's group developed a plant-rendering program which makes use of L-systems, or parallel rewriting systems. These systems bear close resemblance to Chomsky grammars, applying production rules to alter parts of an object. In this case, the objects being acted upon by the L-systems are the segments of an axial tree, a special type of rooted tree whose segments are aligned into long, straight "branches". The L-system productions systematically replace branch segments in an axial tree with increasingly complex groups of segments, thus simulating the increasing complexity of a growing plant.

By attaching attributes to the productions, manipulating their context-sensitivity, and and altering the specific details of the rules, Prusinkiewicz's group can obtain a wide variety of plant shapes in different developmental stages. The axial tree representing a plant is rendered using a "turtle" similar to that used in LOGO; tree segments and attributes are interpreted as rendering commands by this turtle. Leaves and flowers can be added to the bare branches at different times and in different orders, simulating observed growth patterns in real-world plants. Even external stimuli can be incorporated into the model to a limited degree, producing realistic deformations of the plant's growth pattern.

Prusinkiewicz's plant growing model makes ingenious use of production rule grammars, something which I have rarely seen used in practice outside of compiler design. This method produces some very nice results, and although Prusinkiewicz limits himself to describing herbaceous plants, the work done here lays a good foundation for further work in modeling wooded plants as well. Despite the realism of the output, however, I would question the usefulness of this program as a realistic model of plant growth suitable for use in biology, one of Prusinkiewicz's stated goals. He has clearly done a lot of research into the physiology of plants, and has made a good attempt to incorporate major elements of plant developmental biology into the model; but even so, the model used here could hardly be considered explanatory in any way.

D. Fowler, et. al., A Collision-based Model of Spiral Phyllotaxis

Fowler et. al.'s model, perhaps even more so than Prusinkiewicz's, produces some spectacularly realistic renderings. However, I also question their calling this model "explanatory", especially since the process of plant organ development still appears to be an open question in biology. The mathematics involved here is simple, clever, produces very accurate renderings, and is clearly more robust that simple geometric rendering; but it seems a bit of a stretch to say that this model explains anything about plant development. (Perhaps this is merely a poor choice of terminology on their part.)

"A Collision-based Model of Spiral Phyllotaxis", by D.R.Fowler, P.Prusinkiewicz and J.Battjes

In this paper the authors present a method for modeling Spiral Phyllotaxis using a collision based model. Spiral Phyllotaxis is the spiral arrangement of plant organs such as leaves, florets, or seeds. Some examples were sited as illustrations; among these were the pineapple and the sunflower. This phenomenon of organs spirally arranging themselves suggests that information is passed not only from the environment to the plant (e.g., the suns rays) but between the organs of the plants themselves.

The collision-based model used describes the distribution of the organs (or primordias) on a receptical (or supporting surface). The receptical is positioned on top of the stalk and can be seen as defining the overall shape of the flower head. The entire approach taken was quite interesting. The authors first began by studying the development of a plant and subsequently implementing a system which imitates (to some extent) the growth behavior. When a plant is in its infancy there exist the primordia which are essentially underdeveloped organs. As the plants grow, the organs grow (as does the recepticle they are embedded in) and turn into flowers or leaves, etc... What does not change as the plant matures is the spiral arrangement of the organs.

The authors model this process by first assuming a fully grown recepticle (modeled as a curve rotated around an axis) and spherical primordia. Where a primordia is placed is such that it forms and angle (assumed) of 137.5 degrees, as seen from the axis of the recepticle, with the previously placed primordia. At some point, the placement of a primordia will result in a collision. At this point the primordia is displace toward the apex of the recepticle. The process is repeated until no more primordia will fit on the recepticle. The primordia are then replaced with models of organs (Bezier surfaces) specific to the plant being modeled.

The method proposed seems very simple and produces excellent results. However, everything looks too perfect. I propose that the introduction of some randomness might solve this problem. However, this could also have the effect of "exploding" the system.  Therefore perhaps the random elements would have to be some predefined set of functions which, with low probability of occurence, are randomly applied based on some distribution.

"Developmental Models of Herbaceous Plants for Computer ImageryPurposes", by P.Prusinkiewicz, A.Lindenmayer and J.Hanan

Because plants are living creatures, there exists some level of non-deterministic behavior in their growth. That is, not all plants of the same species look alike just like the fact that not all humans look alike. A plant develops, not only according to influencing factors of its surrounding environment, but according to some genetic pattern. Therefore, the modeling of a plant goes beyond that of simply modeling an object and into the domain of modeling an evolutionary process (i.e., from seedling to full grown specimen).

The authors propose a method for modeling herbaceous plants for obtaining realistic representations of plant as well as for obtaining animations describing a plants evolutionary process. They achieve this through the use of L-Systems, a model of development proposed by Lindenmayer. The L-system model is based on rewriting rules, otherwise known as productions. The plant is modeled as an axial tree which is defined according to specific rules about node placement and branching behavior. The plants evolve by replacing entire segments with new, more complicated segments. This replacement, or rewriting is done according to an L-System model.

The authors go into quite a bit of detail and give many examples of their approach. The paper is structured in such a way that we start with very simple plant models and progress to quite complicated expressions. A main point addressed was that there exists qualitative changes in development behavior that can be observed over time (or at certain times) and this must be accounted for. Some way was needed to specify this switch in behavior. The authors present three possible methods, (1) a delay mechanism whereby a segment does not switch its behavior until it has reached a certain state, (2) a stochastic mechanism whereby a segment has a certain probability of switching into a state and (3) providing different sets of behaviors whereby the segment switches from one set to another. Additionally, variation is added to species of plants using the stochastic mechanism so that all species of plants will not be identical.

The results were impressive, perhaps because initial research was done for each herbacious plant being modeled to determine its structure and growth behavior. Modeling nature is an interesting problem. It would be interesting to see the results of producing hybrid species of plants and seeing if the results are what we would expect.

Developmental Models of Herbaceous Plants for Computer Imagery Purposes

My original critique was going to be that this paper was only loosely grounded in physics, but after reading all the way through (and looking at the title) I realized that the goal was just to make plants that looked good. That result seems to have been accomplished (even though I don't have a good copy of the resulting slides). The model used for a plant is a tree L-system, which is a graph with rules defined for re-writing. Embedded in the L-system are control mechanisms for controlling plant development. Basically, by changing the rules for the control mechanisms the authors have been able to simulate the development of a myriad of plants using this system. Applying models for organs, textures, etc. to these L-systems (as well as introducing some randomness to the development) create very realistic looking plants. I think that this model is extremely useful, and can continue to be useful because the basic framework (the L-system) will always be as accurate as it was in 1988. And to improve the quality of the rendered plants, you only need to improve the textures and polygon models for the plant parts, and little change should be needed to the underlying framework.

A Collision-based Model of Spiral Phyllotaxis

This paper offers a real physics-based approach to modeling flowers with incredible results. By carefully modeling collisions of primordia (undeveloped florets and organs) at the "microscopic" level, the authors have been able to realistically model the arrangement of a flower capitulum (flower head). Then replacing the primordia with developed plant organs yields amazingly realistic and beautiful flowers. It seems to me that these two papers' authors should get together and combine work to make truly great plant and flower models. Of course, this paper seems to fall away from the physical basis when it comes time to go from the capitulum to the finished flower.

Two approaches to the problem are mentioned, one of them works directly with the definition of branching structures using geometrical elements like length of branches and branching angles. The other one defines the plant topology as the base for building the object.

Plants are defined by a small set of rules applied repetitively to produce more complex structures. The spatio-temporal attributes that this method present, make it possible to create temporal forms that give the impression of plant growth. This technique simulates the development and at the same time considers it the basis of realism, the main idea is to think of the form as a event in space-time.

Using this approach they are getting a natural modeling of the space time relation between plant parts (so that various developmental stages in the same plant can be observed at the same time). Also they obtain a model to animated growth sequences that is at least mathematically correct, although they say "biologically correct".

This approach does not consider woody plants because their form is determined by the environment, competition between branches and accidents, this event are not modeled by this paper. Herbaceous plants are used because of the predominant role of their int ernal control mechanism to their development. This make it more realistic the assumption of non external agents interacting in the process, at the same time it simplifies the model considerably.

The method uses L-systems, grammars, general rewriting systems, geometry and object modeling, very computer-science-related concepts.

They are modeling the process in which some segments of the plant are transformed into more complex structures with a graph rewriting mechanism which uses the axial trees. An edge is replaced by an axial tree by a rewriting rule or grammar production.

Also they are using a parallel operation, which is an excellent idea. Parallel rewriting (L-systems)is more appropriate for simulating biological development because it takes part everywhere at the same time in the organism.

Using L-systems: lineage (transference of genetic info. from ancestor to descendants) is represented by context free productions, interaction (exchanging info between neigbouring cells) is represented by context sensitive productions.

It is necessary to specify geometric and graphical aspects of the objects, they do this by giving geometric meaning to the symbols they use in the grammar. These attribute symbols perform rotation, turns, pitching, angle increments, etc. **Something inte resting is that in this way they can use tropism vectors that can modify the action of the basic geometric attributes in the plant.

They provide some examples of variations of the basic structures, they talk about the use of racemes, the use of delays (one lateral branch may start growing before the other), how to model qualitative changes in the middle of developmental processes (or how to have not only homogeneous sequences but sequences that can change with the time). In order to avoid the artificial regularity when generating plants with deterministic L-systems, they introduce stochastic L-systems to create variation but preservi ng general aspects.

With respect to the modeling of surfaces and volumes to give real aspect to the skeletal tree already modeled, they use an approach that consist of filling polygons made of lines defined by an L-system, in some cases they use a tree structure to define su rface.

In general I think that their idea of generating realistic plants images by simulating its development is very neat. Using the nice correspondence between L-systems and plant structure is very elegant and give some simplicity to the model. They are also u sing the same structure to modeling the geometry and other biological aspects. Certain artificial aspects were included in modeling the delays ( the result is a deterministic state), I think that this could be done more biologically oriented by using prob ability distributions obtained from other studies on plants (for example on branch development) and write grammars that use them. I particularly liked some details like the modeling of environmental change and other real events. They just switch between grammar 'tables' but something can be done to avoid it and make it a more autonomous process. As part of the conclusions, they provided very good ideas to improve this work, in my opinion addition of texture and decoupling the time definition from the L-s ystems are the most important ones.

This paper analyzes the common effect called spiral pyllotaxis present in the arrangement of plant, basically the presence of spiral patterns.

This work basically deals with the modeling of this effect based on detecting and eliminating collision between the organs. Phyllotaxis is characterized by conspicuous spirals or parastichies, formed in a structure of sequences of adjacent organs. It is a lso know that the number of parastichies running in opposite direction are two consecutive Fibonacci numbers and their divergence angle is close to 137.5o.

There are two main approaches for modeling this effect. Descriptive models characterize spiral arrangement of organs with the same size on the surface of a disk or cylinder, but in nature organs vary in size and the surface where they lie is not normally ideal disks or cylinders. Explanatory models consider the dynamic process controlling the formation of the pattern, but no universally accepted model has been proposed. The main idea is that the spirals result from local interaction between developing or gans, mechanically pushing each other.

What this paper presents is a model based on collision that combines both components. They developed a model to simulate the effect of canalization in Microseris to model phyllotaxis, without many of the restrictions commonly present. The main aspect: It works on organs/receptacles of arbitrary size and shape.

Basically the receptacle is viewed as a surface of revolution, generated by a curve rotated around a vertical axis. Primordia are added to the structure using the divergence angle (137.5), their centers are constrained by the receptacle. Once there is no more space on the base of the receptacle, a new ring is formed and the primordium is placed on the tangent to its closest neighbor. This process terminated when there is no more room.

**Something important is the fact that in order to simplify the model they are developing the primordia in an already developed receptacle. In nature the differentiation is concurrent with the receptacle's growth. But, according to its authors, it corresp ond with the microscopic observations.

With respect to the computer implementation, the pattern is formed by placing spheres on a receptacle, then the spheres are replaced by a realistic model of organs. So the real organs have different shape. When placing the organs, they represent each one by a contact point and a pair of orthogonal vectors.

They obtained beautiful and realistic images with a good level of visual complexity and natural appearance. I seemed that the technique can run fast enough to perform interactive changes.

It seems to be a very useful model, specially when dealing with realism in plant modeling, although this effect can also be found in different environments. It can be used to synthesize a wide range of natural plant structures. It Arranges organs of vary ing sizes on arbitrary surfaces of revolution. Their collision model is based on sphere collision, when they deal with it, they also optimize the packing of the structures. I think they are not modeling the development (directly), they cannot show it bec ause they are assuming an already developed receptacle.

Stan Sclaroff

Created:  Jan 21, 1997

Last Modified: Jan 30, 1997