Our next topic is flower modeling. This is an example of very domain specific modeling operations. And the work we introduce here is called floral diagrams and inflorescences. The problem we present here, discuss here is flower modeling, and flower modeling is very difficult. It has very complicated geometry. With you know, petals and sepals, and also, at the same time, complicated structure. So, again, each element has complicated shape, and also we have a very complicated arrangement of interior elements. So that's the problem we want to address. And our approach is like this, for handling complicated geometry we use very specialized tailored sketch interfaces for individual- for all our elements. For handling complicated structure we again, provide a very specialized structure editor. By combing a very specialized system we can make it very much easier for the user to design various kinds of flowers. Let me show you a video. So here's a problem we would try to address. You know, this kind of flower diagram- flower models consists of many small elements obligated together. And then we have complete skeleton structure like this one, and like this one. [BLANK_AUDIO] And then what we do is use a traditional representation called floral diagrams, and inflorescences as an interface for designing our flowers in a computer. [BLANK_AUDIO] So floral diagram, defines arrangements of elements for individual flower. [BLANK_AUDIO] Inflorescences defines an arrangement of aggregation of flowers into this model. And as you see, user can interactively operates the diagram, and then you continuously see the updated geometry [BLANK_AUDIO] And the modeling process start with the defining of a floral diagram. So in the flower base you arrange individual elements, and then you can see a 3-D measure preview here. [BLANK_AUDIO] So as you see, this is a very specialized dedicated modeling system for flower arrangements. [BLANK_AUDIO] After our getting a diagram, now, the user defines a geometry. As you see, we provide a very, very simple sketching interface for defining a shape. But here, system automatically generates a surface of revolution And for each floral element, our system provides a very dedicated sketching interface. So this one is generating I think is a- sepals [BLANK_AUDIO] And then this is a petal modeling, so you draw three lines. And then you get- instantly get a 3-D model. And from the side view a user draws a line, and you get a deformed shape. So with just only four strokes, you will get a very huge form of flower element. And you can continuously add more and more strokes, to get more detailed shape. And then after having floral diagram and 3D components, you establish correspondences, associations, and then with that information our system start to generate an aggregated composition. And then you will get a beautiful shape this way And now we assemble them together into a, structure using inflorescences. So you get this template, and then you change the shape, and then you will get the shape. And now we define axis, center axis by sketching. This is an interesting part, so you draw two dimensional stroke to define axis, and then system generates 3-Dimentional axis let me see. So user draw a stroke, and then as user draw, system would automatically generate a 3- dimensional axis. As soon as you finish drawing you can rotate and you will get the reasonable 3D shape. [BLANK_AUDIO] Yeah, so here's a little bit more description about 2D input to 3D stalk part. So without depth assignment if you project your input into a flat surface it looks like very unnatural, a very flat shape. However, with our algorithm. User draws a stroke, two-dimensional stroke, and the system automatically assigns a natural, naturally looking depth variation, so if you look from, look from a sideway, it looks natural. So to do this, what we do is to assume that three-dimensional curvature is always constant in 3-D space. With this assumption we can efficiently compute the depths. And then here’s a couple of results. I think it is very tedious and time-consuming to generate these kinds of models using traditional 3D general purpose 3D-modeling systems. But with our system, it's very, much, much faster. Of course, it takes certain time, but it's much faster than using traditional methods. And you can easily modify them. [BLANK_AUDIO] Yup, that's it. And then, here’s a couple of results. So these are 3-Dimentional shapes and these are the structure editors. And then here let me briefly describe the algorithm of 2D stroke to 3D shape. And how to infer depths. Here’s a little bit of details. So as I said the basic assumption. The main idea is to assume constant curvature in 3-D space. Which means second derivatives, x-position and second derivative of zed- z positions by y value, is constant. Y is a growth direction. See here again, this is two-dimensional input on X-Y plane. Y is growth direction, and x is sideways vectors and then we compute, we try to compute z values in this way. So in order to do it, first we project strokes onto x-y plane and resample. So we put the sample points here, and then we suppose that 3D curvature is constant so. Second derivative of X along Y and second derivative Z along Y equal constant. And we know this value by this shape. And we also assume this constant value by maximum of this value, probably somewhere like here. Maximum curvature. And here. The curvature in X-Y plane gets smaller here. But instead we at, assign large value here, which means large curvature in Z directions, like here. So this is given value, and this is given value, and you get this value. And after get these values second derivative of Z, then we just integrate twice, and then you will get the values, so that is the algorithm. So to learn more, the original paper can be found in SIGGRAPH 2005 titled Floral Diagrams and Inflorescences. Interactive flower modeling using botanical structural constraints. And plant modeling has a long history of research, and one famous book is called The Algorithmic Beauty of Plants, and this one discusses lots of interesting techniques to get 3D models by rule-based systems. So here is a, one example, you draw this kind of synthesis rule, and you will get this kind of very complicated structure, and this is very beautiful mathematical system. However, it is a little bit unintuitive for our artists to design model. So recent-recently people use this kind of graphical rule editor to generate a 3D shape like this. And this, and this paper about the paper titled, Modeling Methods and User Interface for Creating Plants, was currently available as a 3D-modeling system called XFrog. And this is a very popular tool. So if you are interested in plant modeling I recommend you take a look at these systems. Thank you.
