This project aim to be a run-time street builder done inside World Wind. This application works drawing texturized shapes accordingly to the position given by the user. The program modifies the terrain taken the elevation from these shapes in order to have a street every time over the terrain. User can: add and remove pieces of shap, add and remove shape, select shapes already present, move points of the street, modify the blend. All these stuff are explained inside this paper.
This project aim to be a run-time street builder done inside World Wind. This application works drawing texturized shapes accordingly to the position given by the user. The program modifies the terrain taken the elevation from these shapes in order to have a street every time over the terrain. User can: add and remove pieces of shap, add and remove shape, select shapes already present, move points of the street, modify the blend. All these stuff are explained inside this paper.
A mashup is a Web application that combines data from one or more sources into a single integrated tool. The goal of the project is the possibility to visualize sustainable restaurants on the territory.
A mashup is a Web application that combines data from one or more sources into a single integrated tool. The goal of the project is the possibility to visualize sustainable restaurants on the territory.
The objective of this project is to implement an application that can define and display the rescue mission path and the areas of interest visible from the different points of view (car, plane, ship) of the rescue team.
The objective of this project is to implement an application that can define and display the rescue mission path and the areas of interest visible from the different points of view (car, plane, ship) of the rescue team.
This report describes an approach of using a “Master-Slave” network communication mechanism by using Java Bindings for OpenGL API (Jogl), based on a real implementation, to achieve the effect of displaying 3D object within multiple screens.
A graphic library and an application for simple curve manipolationgraphitech
The project consists in a software that uses a developed library in the Intermediate project to construct complex functionalities.
The functional asked requisites are:
1. Load a picture in background.
2. Generate different kinds of curves using points generated by mouse:
a. Hermite Spline,
b. Bezier Spline,
c. BSpline,
d. Lagrange.
In this way we can isolate the perimeter of the previous loaded picture.
3. Move single points using the mouse drag property.
4. Select multi points and move them together.
5. Curves must be connected to each other.
6. Save the composition of curves in a file.
7. Load the composition of curves saved before.
8. Load a point file ad interpolate the points using the available curves. In this way we can observe the differences generated when same points are interpolated by different kind curves.
9. Change in real time the kind of curve that interpolates a set of points.
This project aim to be a run-time street builder done inside World Wind. This application works drawing texturized shapes accordingly to the position given by the user. The program modifies the terrain taken the elevation from these shapes in order to have a street every time over the terrain. User can: add and remove pieces of shap, add and remove shape, select shapes already present, move points of the street, modify the blend. All these stuff are explained inside this paper.
A mashup is a Web application that combines data from one or more sources into a single integrated tool. The goal of the project is the possibility to visualize sustainable restaurants on the territory.
A mashup is a Web application that combines data from one or more sources into a single integrated tool. The goal of the project is the possibility to visualize sustainable restaurants on the territory.
The objective of this project is to implement an application that can define and display the rescue mission path and the areas of interest visible from the different points of view (car, plane, ship) of the rescue team.
The objective of this project is to implement an application that can define and display the rescue mission path and the areas of interest visible from the different points of view (car, plane, ship) of the rescue team.
This report describes an approach of using a “Master-Slave” network communication mechanism by using Java Bindings for OpenGL API (Jogl), based on a real implementation, to achieve the effect of displaying 3D object within multiple screens.
A graphic library and an application for simple curve manipolationgraphitech
The project consists in a software that uses a developed library in the Intermediate project to construct complex functionalities.
The functional asked requisites are:
1. Load a picture in background.
2. Generate different kinds of curves using points generated by mouse:
a. Hermite Spline,
b. Bezier Spline,
c. BSpline,
d. Lagrange.
In this way we can isolate the perimeter of the previous loaded picture.
3. Move single points using the mouse drag property.
4. Select multi points and move them together.
5. Curves must be connected to each other.
6. Save the composition of curves in a file.
7. Load the composition of curves saved before.
8. Load a point file ad interpolate the points using the available curves. In this way we can observe the differences generated when same points are interpolated by different kind curves.
9. Change in real time the kind of curve that interpolates a set of points.
This report presents the design and the architecture of a java library that allows the final user to interact with applications through non conventional devices, like the Nintendo Wii® Controller (WiiMote), the microphone and the webcam. It has been developed as a java API, that can be easily integrated inside any kind of software that is suitable to be controlled by devices different from a keyboard or a mouse. In particular in this report we will show how it has been used inside
WorldWind sdk, the open source NASA world exploring tool.
A graphic library and an application for simple curve manipolationgraphitech
The project consists in a software that uses a developed library in the Intermediate project to construct complex functionalities.
The functional asked requisites are:
1. Load a picture in background.
2. Generate different kinds of curves using points generated by mouse:
a. Hermite Spline,
b. Bezier Spline,
c. BSpline,
d. Lagrange.
In this way we can isolate the perimeter of the previous loaded picture.
3. Move single points using the mouse drag property.
4. Select multi points and move them together.
5. Curves must be connected to each other.
6. Save the composition of curves in a file.
7. Load the composition of curves saved before.
8. Load a point file ad interpolate the points using the available curves. In this way we can observe the differences generated when same points are interpolated by different kind curves.
9. Change in real time the kind of curve that interpolates a set of points.
A graphic library and an application for simple curve manipolationgraphitech
In this report I am going to describe the implementation of a simple curve manipolation application, developed as a fullment of the second project for the course of Principles of Computer Graphics. The report is organized as follows: Section 1 introduces the problem and what the application should implement, Section 2 describes the architecture of the program, Section 3 explains some foundamental parts of the source code and nally Section 4 illustrates how to use the application together with some screenshots and examples.
This report describes an approach of using a “Master-Slave” network communication mechanism by using Java Bindings for OpenGL API (Jogl), based on a real implementation, to achieve the effect of displaying 3D object within multiple screens.
This report presents the design and the architecture of a java library that allows the final user to interact with applications through non conventional devices, like the Nintendo Wii® Controller (WiiMote), the microphone and the webcam. It has been developed as a java API, that can be easily integrated inside any kind of software that is suitable to be controlled by devices different from a keyboard or a mouse. In particular in this report we will show how it has been used inside
WorldWind sdk, the open source NASA world exploring tool.
These easy-to-follow tutorials will introduce you to the features and benefits of FastTrack Schedule 10 project management software. The tutorials will guide you through FastTrack Schedule’s core functionality as well as scheduling your project, creating dependencies, tracking progress, using the work calendar, managing resources, consolidating projects, and much more.
Learn more about FastTrack Schedule 10 and download a free trial version at http://www.aecsoftware.com
This report presents the design and the architecture of a java library that allows the final user to interact with applications through non conventional devices, like the Nintendo Wii® Controller (WiiMote), the microphone and the webcam. It has been developed as a java API, that can be easily integrated inside any kind of software that is suitable to be controlled by devices different from a keyboard or a mouse. In particular in this report we will show how it has been used inside
WorldWind sdk, the open source NASA world exploring tool.
A graphic library and an application for simple curve manipolationgraphitech
The project consists in a software that uses a developed library in the Intermediate project to construct complex functionalities.
The functional asked requisites are:
1. Load a picture in background.
2. Generate different kinds of curves using points generated by mouse:
a. Hermite Spline,
b. Bezier Spline,
c. BSpline,
d. Lagrange.
In this way we can isolate the perimeter of the previous loaded picture.
3. Move single points using the mouse drag property.
4. Select multi points and move them together.
5. Curves must be connected to each other.
6. Save the composition of curves in a file.
7. Load the composition of curves saved before.
8. Load a point file ad interpolate the points using the available curves. In this way we can observe the differences generated when same points are interpolated by different kind curves.
9. Change in real time the kind of curve that interpolates a set of points.
A graphic library and an application for simple curve manipolationgraphitech
In this report I am going to describe the implementation of a simple curve manipolation application, developed as a fullment of the second project for the course of Principles of Computer Graphics. The report is organized as follows: Section 1 introduces the problem and what the application should implement, Section 2 describes the architecture of the program, Section 3 explains some foundamental parts of the source code and nally Section 4 illustrates how to use the application together with some screenshots and examples.
This report describes an approach of using a “Master-Slave” network communication mechanism by using Java Bindings for OpenGL API (Jogl), based on a real implementation, to achieve the effect of displaying 3D object within multiple screens.
This report presents the design and the architecture of a java library that allows the final user to interact with applications through non conventional devices, like the Nintendo Wii® Controller (WiiMote), the microphone and the webcam. It has been developed as a java API, that can be easily integrated inside any kind of software that is suitable to be controlled by devices different from a keyboard or a mouse. In particular in this report we will show how it has been used inside
WorldWind sdk, the open source NASA world exploring tool.
These easy-to-follow tutorials will introduce you to the features and benefits of FastTrack Schedule 10 project management software. The tutorials will guide you through FastTrack Schedule’s core functionality as well as scheduling your project, creating dependencies, tracking progress, using the work calendar, managing resources, consolidating projects, and much more.
Learn more about FastTrack Schedule 10 and download a free trial version at http://www.aecsoftware.com
All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.
Orangescrum Gantt chart Add on User ManualOrangescrum
Orangescrum Gantt chart add-on user manual will help you to know the installation guide for Gantt chart add-on & the features of Gantt chart add-on.
Open source project management tool, Orangescrum Gantt chart add-on: Highly interactive graphical view of multiple tasks, their dependencies, and timelines on a single platform. For more details, please visit: https://www.orangescrum.org/addon-details/ganttchart
Explore the Orangescrum Gantt chart add-on demo at http://newui.orangescrum.org/
The objective of this project is the extension of the framework WorldWind to allow the user to interact directly with the terrain through a series of specially developed tools.
The objective of this project is the extension of the framework WorldWind to allow the user to interact directly with the terrain through a series of specially developed tools.
YARCA (Yet Another Raycasting Application) Projectgraphitech
The scope of this project is to extend NASA’s World Wind to make it possible to visualize ray casting not only in intersection with the terrain, but also to consider 3D objects, which we call barriers, that will be hit by rays emitted by other objects which we call transmitters, calculating the coverage area and field of view of the transmitters and showing how the transmission signal is reflected onto the objects’ surfaces.
YARCA (Yet Another Raycasting Application) Projectgraphitech
The scope of this project is to extend NASA’s World Wind to make it possible to visualize ray casting not only in intersection with the terrain, but also to consider 3D objects, which we call barriers, that will be hit by rays emitted by other objects which we call transmitters, calculating the coverage area and field of view of the transmitters and showing how the transmission signal is reflected onto the objects’ surfaces.
Implementation of Hybrid Terrain Representation in Nasa WorldWind: Regular Gr...graphitech
In this project we incorporated the use of a TIN inside WorldWind's regular grid. Direct rendering of both the regular grid and the TIN would generate geometric discontinuities. We used several methods to eliminate these discontinuities.
Implementation of Hybrid Terrain Representation in Nasa WorldWind: Regular Gr...graphitech
In this project we incorporated the use of a TIN inside WorldWind's regular grid. Direct rendering of both the
regular grid and the TIN would generate geometric discontinuities. We used several methods to eliminate
these discontinuities.
The project described in this report, called affectionately "JOGLnoid", corresponds
a clone of the famous arcade game "Arkanoid". The game was developed through the assistance of the OpenGL graphics library.
Extended Navigation Mode in NASA World Wind Javagraphitech
World Wind is an open source 3D interactive world viewer created by NASA. This project has extended the basic navigation mode in World Wind version 0.4.1 to include the following:
- Look left & right
- Look up & down
- Change the altitude of the camera
- Fly mode (mouse only)
The report discusses my version of the arcade game Arcanoid. My version of
Arcanoid is developed as the project for the Computer Graphics course. The
report presents the logic and concepts for building the geometries, navigation,
collision detection and reflection techniques used to build my version of the
game. It also lists the features available in my version of the game.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
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Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
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Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
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This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
How libraries can support authors with open access requirements for UKRI fund...
Street Builder
1. Stefano Tranquillini
Street Builder
Raffaele De Amicis, Giuseppe Conti Principi di Computer Grafica – UNITN 08‐09
2.
3. Summary
Abstract ....................................................................................................................................................................6
Street Builder ............................................................................................................................................................6
Library used ..........................................................................................................................................................6
Interface ...................................................................................................................................................................6
Load and Save .......................................................................................................................................................7
Add .......................................................................................................................................................................7
Edit ........................................................................................................................................................................7
Pick........................................................................................................................................................................7
Move .....................................................................................................................................................................7
Delete ...................................................................................................................................................................8
Setting ...................................................................................................................................................................8
The Project’s file .......................................................................................................................................................8
Street ....................................................................................................................................................................8
Shape ....................................................................................................................................................................8
Street ................................................................................................................................................................8
Guard rail ..........................................................................................................................................................9
The classes ............................................................................................................................................................. 10
How Project Works ................................................................................................................................................ 10
Construction of a street ..................................................................................................................................... 10
Modification of points ....................................................................................................................................... 15
Modification of the terrain ................................................................................................................................ 16
Rectangular Tessellator ................................................................................................................................. 16
ModifiedTerrain ............................................................................................................................................. 20
TerrainBoundary ............................................................................................................................................ 21
Some Results and image ....................................................................................................................................... 22
.
Modification of terrain ...................................................................................................................................... 22
Line construction ............................................................................................................................................... 23
Blend .................................................................................................................................................................. 23
Tile density ........................................................................................................................................................ 25
.
Conclusion ............................................................................................................................................................. 26
Possible extension ............................................................................................................................................. 26
6. Abstract
This project aim to be a run‐time street builder done inside World
Wind. This application works drawing texturized shapes accordingly
to the positions given by the user. The program modifies the terrain
taken the elevation from these shapes in order to have a street every
time over the terrain. User can: add and remove pieces of a shape,
add and remove shape, select shapes already present, move points of
the street, modify the blend. All these stuff are explained inside this
paper.
Street Builder
Library used
Inside this project I’d use:
• World Wind source by NASA. Use the modify package (jar)!
• JTS: java topological suite.
• JOGL: a binding of OpenGL in java.
• SimpleFramework to store and load XML.
Interface
7.
Load Save Add Edit Pick Move Delete Setting Information
• Load: permits to load shape or shapes from file.
• Save: store shape or shapes into a file.
• Add: Adding a shape (street).
• Edit: adding or removing pieces of the shape.
• Pick: select a shape.
• Move: permits to move the points of the street, and the Bezier control point.
• Delete: remove the current shape.
• Setting: change the setting of the system.
Load and Save
The user can select or specify the file to store or load.
Add
This interface appears when a user tries to add a shape. The user
can select the type of the street and the type of the guardrail.
As we can see, each street has a different texture and dimension.
Same thing for the guardrails.
All these information are store into a XML file.
Edit
The user can works on the current shape. If no shape is selected the add dialog is displayed and the user can
specify the new shape to add. The edit functionality permits to:
• Add a piece: simply click on the terrain with the left mouse button
• Remove a piece: Clicking by the right mouse button
Pick
This function permits to select a shape. When is activates and the mouse rollover a shape the shape become
green. If the user click on the shape, the shape become the current shape and the user can work on it.
Move
Clicking on this button, the system shown points on the current shape, points for: start and end pieces, 3 points
for the Bezier.
If inside setting, snap is enabling, the points of the street can be moved only on the middle line of the pieces.
8. NB: Bezier point can be:
• Move: Simply click and drag the point
• Rotate: Press and hold the “A” button and drag the point.
• Resize: Press and hold the “S” button and drag the point.
These last three functionalities are given to let at the user a way to have a better result.
Delete
Remove an entire shape. When a shape has to be removed a prompt is shown and the street becomes green.
Setting
This is the setting’s dialog, the user can specified:
• The numbers of points that will be add at the current tile density.
• If shown or not the current shape
• If shown or not the interior boundary (grid)
• If the points have to be snapped: the points is moved on the line of the quad,
otherwise the movement is freehand.
• If has to be shown the construction line. (see the results section )
• The path of the skirt Texture
• The path from where load the shape configuration.
When click on save these information are stored into a file.
The Project’s file
Al lots of stuff are stored in files: shapes’ setting and the streets done by the user.
Street
In order to store the street the system serialize a class that aim to transport the information of the street.
Shape
There are two type of shape: street and guardrail. To add new shape need to construct a new file that follows
the structure above.
Street
<shapeConfig> Contains:
<path>shapecity.png</path> The texture path
<delta_width>6.0</delta_width>
<name>City Street </name>
The dimension
<description> </description> The name and a description.
</shapeConfig>
9. Guard rail
<guardrailConfig> Contains:
<texGuard>shapeguardrail1.png</texGuard> The texture path
<dimGuard>1.0</dimGuard>
<name>GuardRail 1</name>
The dimension (elevation)
</guardrailConfig> The name and a description.
10. The classes
This section contains a brief explanation of the classes. To have a better explanation looks on the JavaDoc or
inside the code.
• Gui: Contains the gui parts (the prompts shown on add and setting)
• Information: Contains a static class (TempAdd). This class is used to
share information into the project
• Main: Contains the main class. This class manages the menu and the
interaction.
• Setting: This package contains the setting parts of the system.
• Shape: Contains the classes that are used to build and render the
shape. Shape is the parent class that contains a list of shapeQuad.
Each ShapQuad is a piece of the street.
• Terrain: This package contains the classes used to modify the
terrain. ModifiedTerrain is the parent class that contains a list of
TerrainBoundary. The RectangularTessellator is a modified version
of the RectangularTessleator done by world wind.
Dragable classes are used to allow the movement of the points.
• UTIL: This package contains the util part of the system
o Listener: The manager of the listener: mouse and keyboard
o Geom: My class that is used to compute line, intersection
and other things.
o Other: Class that allows a simply way to load stuff
How Project Works
In this section there’s the explanation about how the project works.
Construction of a street
The construction of a street is done in two different ways. The first time is a simple construction of a rectangle
around a line (see image 1, 2 and 3). When a new piece is added the previous quad is cut and the new quad is
added. Between these two quads a number of quads are added as connectors that are used to construct a
blend.
14. The result.
NB: the vertexes are named in this way. The Boundary indexes
are 2 and 3 near the start position and 0, 1 near the end. This
is done by JTS that give us the boundary in this way.
This figure is useful to understand how the algorithm for the
newPieces works and how the vertexes are attached.
These entire steps are done using a Meters coordinates, WW works in lat Lon (angle) and so, inside the render,
there’s a converting of the coordinate in latlon done using a class PositionUtil:
private Position fromUTMtoPosition(Position p, Coordinate e)
Inside the converting step there’s the calculation of the guard rail points done taken the boundary of the street
and computing points that has an elevation plus the elevation of guard rail.
In render step, each quad render a skirt from the boundary of the street to the center of the earth.
15. The guardrail and the skirt.
The skirt is shown better in the following image.
Modification of points
The project permits to modify the point of the street. Clicking on button, on the shape appears some points,
these points’ permits to move the pieces of the shape or the Bezier points.
When a point is moved, the system recalculates all the connectors and the new vertices. These steps are done
in the render.
17. The creation of the ModifiedTerrain
if (Setting.showInterior == this.makeTileSkirts) {
this.makeTileSkirts = !Setting.showInterior;
WorldWind.getMemoryCache(CACHE_ID).clear();
dc.getModel().setShowWireframeInterior(Setting.showInterior);
}
This part is done to shown the interior Wireframe without the skirt. If there’s a change remove all the cache
and recomputed all the tiles
MemoryCache cache = WorldWind.getMemoryCache(CACHE_ID);
CacheKey cacheKey = this.createCacheKey(dc, tile, resolution);
18.
Read the cache of WW
if (!TempAdd.toRemove) {
tile.ri = (RenderInfo) cache.getObject(cacheKey);
if (tile.ri != null) {
return;
}
} else {
ModifiedTerrains.clear();
cache.clear();
cacheKey = null;
}
If there’s a modification (a pieces is added or removed: the ELSE branch) remove my cache and all the cache.
Otherwise (the IF branch) load the information already present.
int totShape = TempAdd.shapes.size();
ModifiedTerrain mf = new ModifiedTerrain();
if (ModifiedTerrains.containsKey(tile.getTileKey())) {
mf = ModifiedTerrains.get(tile.getTileKey());
} else {
//construtct all.
mf = new ModifiedTerrain();
for (int i = 0; i < totShape; i++) {
Shape Shape_now = TempAdd.shapes.get(i);
if (tile.sector.intersects(Shape_now.sector())) {
int tot_pice = Shape_now.pieces.size();
for (int j = 0; j < tot_pice; j++) {
TerrainBoundary sq = Shape_now.pieces.get(j).terrainBoundary;
if (tile.sector.intersects(sq.sector())) {
mf.addTerrainBoundary(sq);
}
Vector<ShapeQuad> connectors =
(Vector<ShapeQuad>)Shape_now.connectors.get(j + "-" + (j + 1));
if (connectors != null) {
int tot_partial = connectors.size();
for (int k = 0; k < tot_partial; k++) {
TerrainBoundary tb =
connectors.get(k).terrainBoundary;
if (tile.sector.intersects(tb.sector())) {
mf.addTerrainBoundary(tb);
}
}
}
}
mf.isModified = true;
}
}
}
This part is the construction of the Modified terrain for the current tile. First check if inside my HashMap
already present the modified terrain, if true: load it. Otherwise recreate all the Modified terrain.
22. Some Results and image
Modification of terrain
The bridge: the terrain is below the line
A cutting of the terrain: the terrain is above the line In these 2 image we can see the difference of delta
23. Line construction
The system allows to shown only the construction
line of a street. You can show using the setting gui.
Blend
Some blend shown by construction line and rendered shape. In 3rd and 4th figure there’s a modification of the
rotation and distance of Bezier points.