4/14/2019
Forest Modelling
v
PA 199 Advanced Game Design
Lecture 8 Procedural Forest and Cities
Dr. Fotis Liarokapis 15th April 2019
A Lot of Variety
Many different tree species present
HCl5»&=-
Species Variation
S
Variation within each species
1
4/14/2019
Procedural Modeling
• Use procedure to generate all needed geometric primitives
• Store complex tasks in procedure
— Detail level
— Shaders
— Internal animation
Procedural Trees
• Trees are a classic example of complex natural objects that can be procedurally modeled
• There have been numerous research papers published on various aspects of botanical modeling
— One recent paper focused on creating the detailed sub-millimeter scale vein patterns seen on leaf surfaces
Procedural Trees.
• By varying a number of key parameters, one can model a wide variety of plants and trees to any level of detail desired
• Even with about 10 parameters, can model a wide variety of overall plant shapes:
— However real plant modeling systems may allow hundreds of parameters as well as the inclusion of custom geometric data to define leaf shapes or branch cross sections
A) Tree silhouette and growth habits B) Branch curving: hyponasty and epinasty QTropisms: notropism, negative gravitropism, plagiotropism, positive gravitropism D) Branch flow: curved, angular E) Gravimorphism: epitony, amphitony, basitony
SimilarTree Forms
Plant Morphology
An important part of a plants morphology is the bud
— A bud is where every part of a plants body starts growing
There are two different types of buds -The apical bud at the end of a branch -The lateral buds
• Can grow new branches, leafs or flowers
2
4/14/2019
Plant Morphology.
• The starting point for leaves (or sub-branches) at a branch is called Nodus
— The part between two nodes is the Internodium
• A node can grow one or more leaves
— The angular distance between all leaves grown at one Node will be constant
Plant Morphology..
• Three basic types:
- (a) One leaf per node, leafs of consecutive nodes are rotated by 180 degrees
- (b) One leaf per node, but consecutive leafs are rotated by the mean building up a spiral shape
- (c) Several leaves per node, leaves alternate
M (b) (c)
(a) (b) (c)
IT**— ®
Primary Shoot Growth
• All plants grow according to the same basic pattern
— Although there is a huge amount of variation within that pattern
• Growth takes place at tips of stems
— Where new leaves are formed
Primary Shoot Growth
Primary growth includes:
— Development of these new leaves at relatively regular intervals
— Elongation of the stem between the nodes
Axillary Growth
At each leaf node an axillary bud is formed
- Which may remain dormant
- Or may develop into a whole new stem
3
4/14/2019
Flowers
2
Flowers will form at the tips of younger stems at certain times of the year, triggered by seasonal properties
- i.e. day length or temperature
Flower petals and other floral components are modified leaves themselves
Plant Shapes
The variety of plant shapes is mainly due to variations in stem shapes, branching properties, and leaf shapes, and these can be broken down into specific properties that can be used to control a procedural plant model
A simple way to model a plant is to start by thinking of it as a bunch of branches (stems) and leaves
Branches
Think of a branch as being a circular extrusion along some path
- But it would certainly be possible to use non-circular cross sections as well
The radius of the cross section will either remain constant or may taper from being thicker at the base and thinner at the tip
— Simplify by specifying a radius at each end and assume a linear interpolation along the branch
Branches
®
The path of the branch can just be a set of points
These points could be a straight line
- Not be hard to add some curvature and randomness
The path could be randomly created just from
- A starting point, an initial direction, and a desired length
Branching
Each branch can spawn off new branches
The new branches would be placed at points along the original branch with some rule to define their initial direction
- For example, it is nice to allow new branches to start at some percentage along the original branch
Branching
The length of the new branches can be defined by two percentages:
— One describes the length of new branches at the base of the original branch
— One describes the length at the tip
The branching angle can be described similarly by values at the base and tip
4
4/14/2019
Branching and Leaves
The branching is usually repeated two or three times so that we get sub-branches on sub-branches on branches
At that point, we branch one final time — But create leaves instead of new branches The leaves can be placed along the branch according to similar rules as sub-branches
2
Shapes of Leaves
@
Details in the Leaf Shapes
(a) (b) (c) (d)
(a)2D leaf without any details, (b) leaf with jagged edges (teeth), (c) leaf with very sharp tip (drip-tip), and (d) leaf warped in 3D space
(a) (b)
(a) Narrow leaves found in bryophytes, pteridophytes, and gymnosperms are slender
(b) Broad leaves found in angiosperms are wide and their thickness is negligible compared to the surface area
5
4/14/2019
(a) (b) (c)
(d) (e)
(a) Straight: the margin is straight (b) Concave: the margin curves towards the primary vein, (c) Convex: the margin curves away from the primary vein, (d) Concavo-convex: the margin is concave proximallyand convex distally. (e) Complex: the margin has more then one point of inflection, (f) Cordate: the margin extends below the base
(a) (b)
(c) (d)
(a) Straight: the margin is straight (b) Convex: the margin curves away from the primary vein (c) Acuminate: the margin is concave proximallyand convex distally or concave only (d) Emarginate: the margin extends above the apex
fpes of leaves based on the position v^ and Max width of the lamina
(c) (d) (e)
(a) Elliptic (b) Obovate (c) Ovate (d) Oblong (e) Linear
Types of Laminar Asymmetries
(a) A simple leaf with asymmetric maximum width (b) A simple leaf with asymmetric cordate base (c) A simple leaf with cordate base on one side and no extension on the other
Common Leave Shapes
11 t • •
Elliptic LiiM Folate I ))....[.. .i-l.ir. Oblong Oval
Obovate Ovate Rhomboidal Orbicular Deltoid
®
Cordate Hcnifonn
Plant Example
6
4/14/2019
Fractal Trees and Plants
2
Fractal trees and plants are among the easiest of fractal objects to understand — They are based on the idea of self-similarity
V W
Fractal Tree Pseudo-Code
DrawTree(n, direction, length)
if n > 0 do DrawTrunk(direction, length) DrawTree(n-l, 3DRandomAngle(direction),
length*Factor(n)) DrawTree(n-l, direction + random % 10, length*Factor(n)) DrawTree(n-l, 3DRandomAngle(direction),
length*Factor(n))
else DrawLeaf()
end if end DrawTree
Branch Strings
Fractal Trees and Plants
The main idea in creating fractal trees or plants is to have a base object and to then create smaller, similar objects protruding from that initial object
— The angle, length and other features of these children can be randomized for a more realistic look
— This method is a recursive method
Fractal Branching Structures
®
Trees and Plants Example
4/14/2019
Grammars and L-Systems
How can we change the structure of something?
— With textures can fake it
To modify the object itself, change its change or add new shapes then need to use L-Systems
less— @ Introduction to L-Systems
• Developed by A. Lindenmayer to model the development of plants
— Originally described cellular growth
• Based on parallel string-rewriting rules
— Formal set of rules and symbols
— Rules applied iteratively to start sequence
• Excellent for modeling organic objects and fractals
L-Systems Definition
The process of replacement can be formalized using a grammar, or parallel rewriting system is called an L-system
IT**— %
L-Systems Structure
• An L-System is a set of three things:
G = (V, w, P )
-V = Alphabet
• Set of symbols that can be replaced
— w = Start or axiom
— P = Set of production rules
L-Systems Structure
L-Systems Physical Interpretation
Variables:    A B Start: A Rules:        A-> B
Process;
1. Take the Start (w) as the current string
2. Apply the production rule to every symbol in the current string.
3. When finished, call this the new string.
4. Repeat
start:
iteration 1: iteration 2: iteration 3: Iteration 4:
<ruleA->B) (rule B >AB) (rules A >B, B >AB) (rules B >AB. A->B, B->AB|
L-Systems can have a physical interpretation, if we assign meaning to letters
The dragon curve drawn using an L-system
8
4/14/2019
Avanon nf mr Ksdl cuvr mrTirn usrsonty rqtil-niigrs
4=re. ri^uu -Jn.i in PUT. * meara turn lift XT mi - means "turn right W 0K turtle gr*(Kcc}
n 0
its I: _n_
F4f.F-F»F
FtF-F-F+F+F+F-F-F-t-F-F-t-F-F-F+F-F+F-F-FtF-i-FtF-F-FBF-t F+F-F-F-tFtF-tF-F-FtF-FtF-F-F*F-FtF-F-FiFtF+F-F-F-tF- F-tFWr-Ftf-iFtf-F-FiF-FtF-F-F-'F'F'F'F-F 'FtF'F-F FtF Ftp F-FtF'F' F F-F -FF'FFF *F-F *F F F'F'FtF F-F»Ft F*F-F-F -F»F'F-F-FtF-FtF-F.F»F.F»F-F. F*F*F»F-F-F-*F
rules : (X   F-|[X)+X)+F[+FX|-X), (F -* FF)
angle : 25°
Here, F means "draw forward", - means "turn left 25°", and + means "turn right 25™ X does not correspond to any drawing action and is used to control the evolution of the curve. [ corresponds to saving the current values for position and angle, which are restored when the corresponding ] is executed.
L-System for Plants
• L-Systems can capture a large array of plant species
• Designing rules for a specific species can be
challenging
A Simple L-System Example
• F [ & + F] F[ - > F] [- > F] [& F]
Parametric Leaf Model
• Coordinate system of the leaf model
• Leaf without basal extension
• Leaf with basal extension
9
4/14/2019
Coordinate system of the leaf model
The parameters of the leaf model are expressed as:
- A right-handed coordinate system with origin at the base
- The y-axis pointing towards the apex of the leaf
- The primary vein is defined to have a unit length
Leaf without Basal Extension
Pi =(0,0),
Pa = (i2,tt0,
Pa = (0,1),
ti = (sin#&, cos(?&),
ta = (0,1),
ta = (— sinft,,cosft,).
Leaf with Basal Extension
PI =	(0,0),
P2 =	
P3 =	
P4 =	(0,1),
tl =	(sin0t,cos#6),
ta =	(1,0),
ts -	(0,1),
ts =	(— sin    cos f)a
Stochastic L-Systems
Specify more than one production rule for a symbol, giving each a probability of occurring
When a stochastic grammar is used in an evolutionary context, it is advisable to incorporate a random seed into the genotype
— So that the stochastic properties of the image remain constant between generations
Other L-Systems
®
A number of elaborations on this basic L-system technique have been developed which can be used in conjunction with each other
Among these are:
— Stochastic
— Context sensitive
— Parametric grammars
Stochastic L-Systems
Several rules for each symbol
Rules chosen based on probability
Create different plants using same L-System
Simulate environmental effects
e. umbc.edu/~ebert/693/TLin/node 18. html
10
4/14/2019
Context Sensitive L-Systems
• A context sensitive production rule looks not only at the symbol it is modifying, but the symbols on the string appearing before and after it
• For instance, the production rule: -b<a>c->aa transforms "a" to "aa"
• Only If the "a" occurs between a "b" and a "c" in the input string: ...bac...
Parametric Grammars L-Systems
• Each symbol in the alphabet has a parameter list associated with it
• A symbol coupled with its parameter list is called a module, and a string in a parametric grammar is a series of modules
• An example string might be: -a(0,l)[b(0,0)]a(l,2)
Context Sensitive L-Systems.
Parametric Grammars L-Systems.
• Parametric grammars allow line lengths and branching angles to be determined by the grammar
— Rather than the turtle interpretation methods
11
4/14/2019
Randomness Definitions
What is Random?
"Having no definite aim or purpose; not sent or guided in a particular direction.."
— Oxford English Dictionary
"Free will is limited to low-level decision making."
— Martin Luther
"God does not play dice with the universe."
— Albert Einstein
48086513282306647093844609S50582231725359408128481117 45028410270193852110S5596446229489S493038196442881097 S66S93344618847S64883378678316S87180190914S648S669234 60348610454386648813393607260249141273724587006606315 58817488152092096282925409171536436789259036001133053 05488204665213841469S1941S116094330S7270365759S919530 98186117381932611793108118848074468379968749867351885 75272489122793818301194912983367336244065664308602139 49463952247371907081798609437027708392171762931767523 8467481846766940813200086818714S863S6088778S771348787 7896091736371787214684409012249S3430146S4958S37108079 22796892589235420199561121290219608640344181398136297 74771309960318707211349999998378978049931089731738816 09631889S0244594SS346908308648S8830883334468S0388619 31188171010003137838788886587833808381480617177669147 3035982534904287554687311595628638823537875937519577
Computer Random Numbers
Plot of the randQ Function
®
Numbers are generated as a sequence, starting from some seed point
Problem is finding the next number so that it has nothing to do with the last
int r - rand();
Randomness in CG
Mountain Forest Example
Typical example is Fractals
"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth.."
Benoit Mandelbrot, (b. 1924)
The Fractal Geometry of Nature, 1982
12
4/14/2019
Spiral Phyllotaxis
2
Fermat's Spiral
Many patterns in nature can be understood with very simple iterated functions
4
A
••••••  000•
oo„° •
n°°0000Oo0o°
o°o0oV0ooO °o°o°o0o0oo°o
Two leaves appear on opposite sides. A third appears between them. The first two push the 3[d away. The result is the golden angle.
Iteration, adding new leaves, settles into the minimization of energy, which results in the golden ratio (angle)
Plant Ecosystems
Very common is the use of a pipeline system to create ecosystems, consisting of a number of succeeding steps such as:
— Terrain Specification
— Distribution Specification/Simulation
— Plant Specification
Plant Ecosystems
Depending on the application there are two steps in generating a virtual ecosystem (can be used alone or in conjunction):
— Generating/specifying plant distributions
— Simulating plant distributions
13
4/14/2019
Sometimes instancing can look pretty good. Pines trees all look similar
lass*— v ligis^^ ®
Terrain and Forest Example City Modeling
14
4/14/2019
SkylineEngine
2
Research oriented project
Aims at the development of a procedural urban modeling engine
http://eee.ude.edu/skvlineEneine/
Pixel City
Written in C++ using OpenGL
No fragment or vertex shaders are used
http://code.eooele.eom/p/pixelcitv/
Pixel City Example
CityScape
®
By PixelActive Features:
- Enhanced road editing capabilities, improved GIS importing, a flexible meta data system, new import and export formats, a redesigned user interface with icons and hotkeys, and performance improvements
The road editing tools add a tangent editor, tunnels, and complex intersections
CityScape Example
CityEngine
Uses maps of population density to create a road network using Open L-systems
- Spaces between blocks subdivided into lots for individual buildings
Buildings generated using parametric stochastic L-systems, detail
m/software/citveneine
15
4/14/2019
City Engine Example
2
V
Environmentally Sensitive L-Systems
So far, L-systems have been more or less self-contained
Parameters provide global influences from the environment
— Provide a way to have the environment affect the development of the system locally
"ivironmentally Sensitive L-Systems Examples
Examples from Synthetic Topiary, by P. Prusinkiewicz, M. James & R. Mech
Open L-systems
®
Generalisation of environmentally sensitive L-systems
When interpreted, control is passed to an external function representing some part of the environment
Environment performs calculations, optionally passes back modified parameter values to be used in the next derivation step
Two-way communication between system and environment
Procedural Road Modeling
Roads can be modeled as cross sections that get path extruded along some curve
The cross section can include:
— Lanes, curbs, sidewalks, center islands Intersections require special handling
— Can still be generated using a set of procedural techniques
Procedural Road Modeling
Roads can be placed on height fields by
placing the control points of the road curves on the height field
— Note that this will require some local flattening for the road and the area to the side of the road
Render road triangles onto the height field
— Where a low detail road is extruded and 'rendered' into the cells of the height field to set their heights
16
4/14/2019
Procedural Road Modeling
Sides of roads can be blended
— Using techniques similar to alpha blending
Note that the above operations will modify the existing shape the height field
— Similarly to how real roads are constructed
V
Procedural Road Modeling
• Ideally, the road surface would be an extrusion and the open terrain would be a height field
• They can be sewn together into a single triangle mesh
— Similarly to how trim curves are used in patch tessellation
Road Modeling Example
^CltyEngine - Road Generation Algorithm
• Uses Open L-systems for road generation
• Environment functions are the constraints imposed on the roads
• Two types of roads: highways and streets
— Highways connect areas of high population density
— Streets connect the rest of the populace to the nearest highway
®
Example of Production Rules for Roads
pi: p2:
p4: p5:
p6: p7:
*(0,   initRuleAttr)?I(initRoadAttr, UWASSIGWED) R(del,   ruleAttr):   del <  0 ^ e
R(del,   ruleAttr)   > ?I(roadAttr,   state):   state == SUCCEED
-> + (roadAttr. angle) F (roadAttr. length) B (dell,   ruleAttrl, roadAttrl) B (del2,   ruleAttr2,   roadAttr2) R(del0,   ruleAttrO)?I(roadAttrO,UWASSIGWED) R(del,   ruleAttr)   > ?I(roadAttr,   state):   state ==
FAILED
-* e
B (del, ruleAttr, ^ B(del - 1, B (del, ruleAttr,
B (del, R(del,
roadAttr):  del > 0 ruleAttr, roadAttr) roadAttr):  del == 0 ;R(del,   ruleAttr)?I(roadAttr,   UWASSIGWED)] ruleAttr,   roadAttr) :  del <  0 -> e ruleAttr)   <  ?I(roadAttr,   state):   del < 0
p8:   ?I(roadAttr,   state): state
^ ?I(roadAttr, state) p9:   ?I(roadAttr,   state): state
UWASSIGWED
= UWASSIGWED
CityEngine Parcel Generation
17
4/14/2019
Population Density
Highways connect peaks on population density map
End of segment shoots rays across map
— Each ray is sampled and sample points look up population value
Highway generation continues in the direction of the fittest ray
Street Patterns
• New York style
— Streets form blocks by restricting the length of a block and the angles that streets follow
• Paris style
— Concentric rings around a central point, connected by short radial streets
• San Francisco style
— Tries to reduce the length of non-contour streets and uses gradient of elevation map
Other Constraints
Modify attributes (length, angle) of road segments in response to surroundings
Make sure roads do not cross water and any other places you'd expect not to find them
Creates intersections with other roads
IT**— %
Road Intersections
• No more dead ends than intersections
• No intersecting segments without creating an intersection (node in the road graph)
• Three rules:
— 2 streets cross: generate an intersection
— Segment ends close to intersection: join it to the intersection
— Segment ends close to another segment: extend it and create an intersection
Buildings Modeling
Once the roadmap has been generated
- Allotments can be generated
- Geometry can be generated
- Buildings can be assigned textures
• Preferably procedural
City Block Divisions
City divided into blocks
Blocks subdivided into allotments
— Blocks assumed to be convex and rectangular
• Concave allotments forbidden
18
4/14/2019
City Block Divisions.
• Simple recursive algorithm
- Divide longest edges that are approximately parallel
-Stop when size less than threshold value
• Allotments without street access or too small discarded
• Maximum building height from image map
Building Geometry
• Parametric, stochastic L-System
• One building per allotment
• Each building style has own set of production rules
• Manipulate arbitrary ground plan
inn
Building Geometry.
L-System modules:
— Transformation modules
— Extrusion module -Branching and Terminating modules -Geometric templates
Final shape is ground plan transformed by L-System
Building functionality not represented
all
Shapes Generation
V
Used by the grammar Consists of:
— Symbol (string)
— Geometric attributes
• Position
• Coordinate System
• Size
— Numeric attributes
Mass Models Generation
Crude volumetric building model Composed of shape primitives
Production Process
v
Configuration: Finite set of basic shapes Start configuration of shapes - Process:
• Select active shape with symbol B
• Choose a rule to compute a successor for B
• Mark B as inactive, add the shapes BNEW to configuration and repeat
Stop when there are no more non-terminals
Assign a picking priority based on detail
19
4/14/2019
Scope Rules
General shape modifying rules — Translate, Rotate, Scale
2
I: A ->-» [ T(0,0,6) S(8,10,18) I("cube") ]
T(6.0,0) S(7,13,18) IC'cube") T(0,0,I6) S(8,15,8) [("cylinder")
Basic Split Rule
Split current scope along one axis — For example:
I:  t'uc -J Suhdivf V"..1.5.0.3.3,3.3){ Hour | ktlje I lltuir | (limr | Hour }
1	0	a	0
m	0	0	0
0	0	0	0
m		0	n
) floor 3.0m ) floor 5.0m
] floor 3.0m } ledge 30cm I floor 3.5m
Scaling
®
Repeat
Relative values can be used
I   floor --> SuMiv(-X",2,1 r. 1 r,2){ B | A | A | B f
S(12, 3) floor -•-
3 [|B| A I A |B
2 4
S(10,3) floor 3 [|B|A|A|B|
2   3   3 2
Tile a specified element - Example:
• Tile as many B elements as possible along X axis
• Number of elements = [x-length/2]
I: floors- Repeat("X",2){ B }
Component Split
Mass Modeling
Split into shapes of lesser dimensions type = type to split
param = associated parameters (if any) {A| ...} = symbol of shape after split
I:       Compdype, param){ A | B | ... | Z }
Union of volumetric shapes — Box, Cylinder, etc
20
4/14/2019
Roofs
2
Facades
Add roof shapes
Categorize different types of roofs — i.e. according to building style or height
Extract 2D facades from 3D shapes Result
- Aligned 2D scope
Grammar refines resulting quads and triangles
Occlusion
Snapping
®
Test for intersections between shapes
None, partial, or full
Avoid placing facade elements on intersections
I: tile : Shape.occ("noparent") == "none" ^ window 2: tile : Sh;ipe.occ("nop;irent") == "part" wall 3: tile : Sh;ipe.occ('"iioparent") == "full"~* £
Additional control of facade layout Used by repeat and subdivide
Repeat
Subdiv
default: snapped:											1
											1
Snap Lines Example
Facade Textures
......i ■ ■
> • ■ 1 ■ I • a
— IB      ■ ■
i  ■ ->,!■■■
......
Division into simple grid-like structures Structures can be layered
::::
Note floor levels are aligned
HRP
21
4/14/2019
Layered Textures
Two base functions form a layer Every layer defines a facade element
2
Layering of Planes
Stacked layers for facade texture
Functions between layers model relation between facade elements
	J		
		tr	
Case Studies for City Modeling
New Classic Buildings of Athens
®
New Classic Buildings Roman Settlements Ionic Temples
Demonstrate how some of the neoclassical buildings in Athens used to be around 100 years ago
- Based on procedural modeling techniques used for the generation of these characteristic buildings
L-System Road Structures
IB| Sub-division of the niac
[Z\ Cored lines before the Transformation (0) Final road grid
ohne edge, straight lines after fl
uilding Topologies and Pavement Generation
-'iJl--i -j y. mml-i   Uuir.Ndiio i>
nasojuniprzahg □□□Dosuoagi. IBpn -rnrj';.: :-.;Ll--,.-|.,i'..'Jn
ju'duoxamucisc "laooaanaizigDrjc
(C) City byautwith blacks
16 f A blark sub-dividpd inlobuildingtopaloKies
■■;".-.■■-i,i.d_i--. r.i 2JstfEfj.Ts:>-|"-ii;,=,hr|,i
±1BHifSSE3!läacaSir.i|f
(DJ City lavautwltti blocks sub-divided nto building tcpologici
V
22
4/14/2019
Building Generation
2
Buildings were done using boxes
— Extruding based on the topologies
Fixed height
-Multiple floors
— Variable number of windows
V
Generation of Building Roofs
Type 3: Flat with ceramics
Balconies, Doors and Windows
Balcony Door Window
Modelling for Roman Settlements
• Automatic generation of Roman cities
• Grammar for describing Roman settlements derived from the writings of Vitruvius including
- Location
- Road structures
- Important building structures
• Temples, theatres, baths and civic buildings
Roman Settlement Planning
• The corners of the city are recorded and the buildable area is marked off
• Next the buildings of significance are added - i.e. forum, theatre, and basilica
• The remaining space is filled with generic structures
23
4/14/2019
Building Placement Methods
Method 1: Random Selection Method 2: Sectioned Districts Method 3: Probability Distribution
The red square marks the centermost point of the city (i.e. the forum), and the yellow squares indicate a special buildings, such as the coliseum or temple. The light, medium, and dark grey squares represent residential structures, religious structures, and governmental structures respectively
Temple Implementation Example
Temple
Repeated Stairs
Altar ][ Cuboid ][ Door ] J
1  Base 1		Roof	
			1
1 Cuboids II		Facade |	Tiles J
Base   ||  Shaft  ]| Capital
Vitruvius Temple Base Definition
Basic Vitruvius roof shape
Vitruvius Temple Cella Definition
Vitruvius Temple Stairway Definition
Vitruvius Temple Column Definition
Results
i      i [
www
r^^n r^^n r^^n , EE I
r.'ijbc com. 23 polygons Crass-section
Tola I
'12 polygon
.I„ii:i '.Ii,■![:■.■
Octagonal column with polygon indents
~~ pnlynnn*.
Computer Graphics
24
4/14/2019
Accuracy Amphitheatre Grammar
Measuring Efficiency
Test was performed on a Toshiba laptop with a 2.3GHz processor, 6 GB of RAM, and a GeForce graphics card
Roman Settlements Video
®
City Radiu: (Meters)
Number of Buildings
Number of Polvgc (triangles)
FPS (Frames P Second)
87970 93610 101952 138146 173660 217226 257074
Accurate Modelling of Temples
Architecture
Accurate modelling of Roman and Greek temples
— Focused on Ionic temples
• Ornaments that usually decorate the column capital have not been taken into account
Creation of a generic tool
— For game developers and archaeologists
eve of cetj , ruir be" of polygons
3Dmudel exporl
25
4/14/2019
Doric and Ionic Columns
Column Shaft Generation
architrave | abacus -
Doric ©1994
lass-*— v fcso^ ®
Column Base Generation Using Bezier Curves
(A) column base subdivided into floors, a is convex and b is concave curvatures (B) A column base constructed using: a) the first b) the second version, figure c) shows
column base subdivided into modules fCa) output using Gl fCb) output using G2 the positions of the control points of a Bezier curve
26
4/14/2019
Accuracy
2
M
Left Image: Comparis capital spiral, Right Ir
m between generated (red) and original (yellow) curves: a) column base, b) column shaft, c) lage: Circles with radius equal to node-curve distance between generated (red) and original (yellow) curves: a) column base, b) column shaft, c) capital spiral
Ionic Temples Video
References
Useful Links
http://www.td-grafik.de/artic/talk20030122/overview.html
http://en.wikipedia.org/wiki/L-system
http://davis.wpi.edu/~matt/courses/fractals/trees.html
http://en.wikipedia.org/wiki/Procedural modeling
Garg, S. Procedural Modeling and Constrained Morphing of
Leaves, DPhil, University of Singapore, 2012.
http://prophet.cs.duke.edU/courses/fall01/cps296.3/resource
s/p351-prusinkiewicz.pdf
Parish, Y., Muller, P. Procedural Modeling of Cities, SIGGRAPH 2011
http://ggg.udg.edu/skvlineEngine/
http://code.google.eom/p/pixelcitv/
http://www.esri.com/software/citvengine
http://algorithmicbotanv.org/papers/#abop http://fractalfoundation.org/ http://vladlen.info/publications/metropolis-procedural-modeling/ http://vterrain.org/Plants/Modelling/
http://www.dpit2.de/navie/index.php?content=p lants
http://forums.odforce.net/topic/16961-procedural-plants-generation-tool/
Questions
27