An object in 3D space

Size: px
Start display at page:

Download "An object in 3D space"

Transcription

1 An object in 3D space An object's viewpoint Every Alice object has a viewpoint. The viewpoint of an object is determined by: The position of the object in 3D space. The orientation of the object relative to a 3D coordinate system. For example, causing the Coach object in Figure 6 to move to a different position or to face in a different direction, or both would change his viewpoint. An object's center point Every Alice object has a center point and three axes. The center point is the position in space (relative to the object) at which that object's three coordinate axes cross. (This is often called the origin.) For example, the center point of the Coach object shown in Figure 6 is a point on the ground midway between his feet, and approximately below the top of his shoelaces. An object's motion If you move an Alice object, you are actually moving its center point. The rest of the object comes along for the ride. (See sidebar.) If you turn an Alice object to the right or to the left, you are rotating the object around one of its three axes. (We will see later that this causes the object to rotate around its green axis.) If you turn an Alice object forward or backward, you are rotating the object around a different axis. (We will see later that this causes the object to rotate around its red axis.) If you roll an Alice object to the right or the left, you are rotating the object around a third axis. (We will see later that this causes the object to rotate around its blue axis.) Think in terms of rotating axes instead of rotating objects A disconnected object Note, however, that it is possible to break the connection between an object and its component parts. For example, you could cause the Coach object to move away and leave his arms behind. When you rotate an object around one of its axes, that axis remains stationary and the other two axes do the rotation. The remainder of the object comes along for the ride. Often when rotating objects, it is easier to visualize rotating two of the axes around a third axis than it is to visualize rotating the object itself. We will see an example of this later when we roll the Coach object's left arm to the right in order to cause him to lift his arm.

2 Italicized method names Why did I represent the words move, turn, and roll in boldface Italics in the above text? I did that to emphasize that I wasn't simply using a generic term for producing motion. Rather I was using a very specific term that has an official connotation. The official connotation is that move, turn, and roll are the names of methods that are used to produce very specific kinds of motion. (You will learn a great deal about methods in subsequent lessons.) Drawing a 3D cube By the time most children reach middle school, they already know how to draw a 3D cube on a sheet of 2D paper. This is true even if they have never had a drawing class. (Does this mean that humans have some inherent knowledge of 3D coordinate systems?) The pictures that they draw are likely to look a lot like Figure 1, or possibly like the yellow outline in Figure 2 without the red, green, and blue lines. Figure 1. A 3D cube. Figure 2. Outline of a 3D cube (note the yellow lines).

3 A 3D coordinate system While those middle-school children probably don't realize it, they are already drawing in a 3D coordinate system. A 3D coordinate system is typically thought of as consisting of three axes where the angle between any pair of axes is ninety degrees. (In mathematical terminology, the axes are orthogonal.) Thus, the three axes are related to one another in the same way that any set of three edges that meet at a corner on the cube in Figure 1 are related to one another. The X, Y, and Z axes Scientists and engineers typically think of the three axes as the horizontal axis (often called X), the vertical axis (often called Y), and a third axis that is perpendicular to the plane formed by X and Y (often called Z). Don't worry, however, because Alice doesn't deal with X, Y, and Z axes. Rather, Alice deals with one axis that runs from left to right, a second axis that runs from bottom to top, and a third axis that runs from front to back.

4 A man with one eye Going back to Figure 1, imagine that a man with one eye is inside the cube. His eye is located at the exact center of the cube and he is facing the inside surface of the medium blue panel. In other words, he is looking directly at the exact center of the medium blue panel with his one good eye. This causes the dark panel to be at his right. It also causes the light blue panel to form a ceiling above his head. A 3D coordinate system in this case would have its origin inside his eyeball. One axis would be sticking out directly in front of his eye (we will refer to this axis as the blue axis). A second axis would be sticking out to his right (we will refer to this axis as the red axis). A third axis would be sticking straight up from his eyeball (we will refer to this axis as the green axis). A picture of the 3D coordinate system described above Now look at Figure 2 and you will see the 3D coordinate system described above. The blue axis in Figure 2 is the axis that would be sticking out directly from the front of the man's eyeball. In fact, if you take a closer look at Figure 1, you can see that blue axis protruding slightly from the center of the medium blue panel. Similarly, the red axis in Figure 2 is the axis that would be sticking out of the man's eyeball toward his right. Once again, a close examination of Figure 1 shows a small portion of that red axis protruding from the dark panel to the man's right. Finally, the green axis in Figure 2 is the axis that is sticking directly up from the man's eyeball. A small portion of that green axis can be seen protruding from the top panel of the cube in Figure 1. Memorize these colors Memorize these colors. In Alice, when you see a blue axis, it is protruding from the front of an object. When you see a red axis, it is protruding from the right side of an object and when you see a green axis, it is protruding from the top of an object. It is important to remember that the directions front/back, right/left, and up/down are relative to the viewpoint of the object, and not relative to the viewpoint of you the viewer. For example, once the object is drawn (rendered) in the world, the right/left, front/back, and up/down directions relative to the viewpoint of that object don't change. If I were to rotate the cube in Figure 1 so as to turn it "upside down", the green axis would then point downward, but that would still be the top of the cube relative to the cube's viewpoint.

5 A penguin diving into the water As another example, I recently created an animation where a penguin walks over to a hole in the ice to dive in. When he arrives at the hole, the green axis is pointing out of the top of his head. He jumps up and rotates in the air (turns forward around his red axis) so that his feet are up and his head is down. At that point, the green arrow is still pointing out of the top of his head but now it points at the water below the penguin. I had to write code to move him "up" to make him fall "down" into the water. The object's center point As mentioned earlier, every object in the gallery has a center point and it may not be where you expect it to be. The center point is the origin where the three axes join with respect to that object's viewpoint. The case for the cube shown in Figure 1 and Figure 2 is straightforward. The center point of the cube is at the exact center of the cube. The center point for a penguin, on the other hand, is at a point in space on the ground midway between the penguin's feet. Many gallery objects have component parts To complicate matters even further, a penguin object is made up of five smaller component objects: head right leg left leg right wing left wing Each of those component objects may contain other component objects. For example, the head contains the following component objects: upper beak lower beak Every component object has its own center point Because the right and left wings of a penguin object are themselves objects, it is possible for us to animate a penguin causing it to flap its wings independently of one another. We can do that by rotating each wing around one of its axes. However, in order for us to figure out how to do that, we must know where the center point is for each wing and we must know what constitutes front, right, and up from the viewpoint of the wing. In other words, we must know the directions of the red, green, and blue axes relative to the center point of the wing.

6 Turn and/or rotate As I explained earlier, if we tell a penguin or any other object, (such as a penguin's wing) to turn to the right or to the left, that object will rotate around the green axis that goes through the object's center point. If we tell an object to turn forward or backward, the object will rotate around the red axis that goes through that object's center point. Finally, if we tell an object to roll to the right or to the left, the object will rotate around the blue axis that goes through that object's center point. As you can see, in order to cause a penguin to flap a wing, we must know the position of the wing object's center point, and we must also know the directions of the red, green, and blue axes that go through the center point for that wing. An airplane example Now consider another example. Take a look at the airplane shown in Figure 3. Figure 3. An airplane with its 3D axes exposed. Suppose we wanted to animate the airplane to make it appear that it is flying in 3D space. Note that the green axis protrudes out of top of the airplane, the red axis protrudes out of the end of the right wing, and the blue axis protrudes out of the front of the airplane. These directions are respectively, up, right, and forward from the viewpoint of the pilot in the cockpit. Airplane motion is complex If we wanted to cause the animation to be realistic, we would need to combine at least two of the three possible rotations for each different type of

7 Make a right turn If we wanted to cause the airplane to make a right turn at the same altitude, we would tell the airplane to turn right. That would cause the airplane to rotate around the green axis. In airplane jargon, this is known as yaw. airplane motion. For example, when an airplane turns to the right or to the left, it doesn't remain level from side to side. In more common terminology, the airplane banks, which is a combination of yaw and roll. Dive toward the ground If we wanted the airplane to dive toward the ground, we would need to tell the airplane to turn forward. This would cause it to rotate around the red axis. In airplane jargon, this is known as pitch. Roll If we wanted the airplane to turn over and fly upside down, we would tell it to roll right or to roll left. That would cause it to rotate around its blue axis. In airplane jargon, this is known as roll. Roll, pitch, and yaw Thus, an object in 3D space can yaw, pitch, or roll, and can do any one of the three in either of two directions. Therefore, the object can experience any combination of the following three rotations: 1. yaw left or yaw right (it cannot yaw left and yaw right at the same time) 2. pitch down or pitch up (it cannot pitch down and pitch up at the same time) 3. roll left or roll right (it cannot roll left and roll right at the same time) Translation In addition to rotation about the three axes, an object can also move (translate): 1. forward or backward (but not both at the same time) 2. right or left (but not both at the same time) 3. up or down (but not both at the same time) Six degrees of freedom More on airplane motion In addition, an airplane always needs to be moving forward in order for the wing surfaces to create lift and cause the airplane to stay in the air. The combination of the three possible rotational motions and the three possible translational motions results in what is often called six degrees of freedom. Thus, Alice objects can be animated with six degrees of freedom (or more if you count the fact that the legs, arms, wings, etc., can experience independent rotation and/or translation while the object to which they belong is also experiencing rotation and/or translation).

8 A little more discussion about the cube Now let's go back and discuss the cube a little more. The surface on which the cube is setting in Figure 1 and Figure 2 is also an object. Thus, it has a center point where its 3D axes join. The center point and the corresponding forward, right, and up axes are shown in Figure 4. (Remember, green is up, red is right, and blue is forward.) Figure 4. Center point of a surface. Can be rotated and translated Just like any other object, the surface can be rotated around any of the three axes, and can be translated in three different directions. There is one major difference, however. If you roll the airplane in Figure 3, it will look like an upside-down airplane. It was created using artwork that was designed to be viewed from any direction in 3D space. The Alice surface shown in Figure 4, on the other hand, was not created with that in mind. Therefore, if you roll the surface, until you turn it upside down, the result won't be very pleasing. A partially transparent version of the cube The cube that you see in Figure 5 is the same cube that you saw in Figure 1. Figure 5. A partially transparent version of the cube.

9 However, in Figure 1, I caused the 3D axes belonging to the cube to be displayed. In Figure 5, I caused the 3D axes belonging to the surface on which the cube is setting to be displayed. In addition, the cube in Figure 1 is 100% opaque while the cube in Figure 5 is only 50% opaque. This makes it possible to see the 3D axes belonging to the surface showing through the cube. In other words, the cube in Figure 5 is 50-percent transparent. (Opacity and transparency are the reverse of one another.) An object's axes travel with the object Every object has a center point and has its own set of 3D axes. The center point and the 3D axes belonging to an object travel with and rotate with the object, independently of the other objects in the world. Thus, the 3D axes belonging to the penguin that I mentioned earlier traveled and rotated with him. When I caused him to turn forward one-half revolution in order to dive headfirst into the water, this caused his green axis, which originally pointed up (from my viewpoint) to be pointing down (from my viewpoint). As a result, I had to move him up to force him to fall down into the water head first. Animating component objects belonging to an object There is one other topic that I want to explain before we leave this lesson. I told you earlier that many Alice objects are composed of other objects and that every Alice object has six degrees of freedom. Even the smaller component objects that make up other objects have six degrees of freedom. However, it may not make sense to exercise all six in all cases. (In real life, an airplane cannot fly backwards, but a helicopter can fly backwards.)

10 Consider a Coach object Consider, for example, the Coach object shown in Figure 6. Figure 6. A Coach object. The Coach object is actually made up of a large number of component objects, each of which has six degrees of freedom.

11 Consider the left arm at the shoulder Let's consider just his left arm at the shoulder joint as shown in Figure 7. Figure 7. Left arm of the Coach object. The coach looks like a headless ghost You may be wondering how I produced the image shown in Figure 7. To begin with, I repositioned the camera so that it would provide a better view of the center point on the left arm, which is what I wanted to see in detail. Then I made his head invisible just to get it out of the way. Then I set the opacity property of the upper body to 30-percent so that we can still see it for reference, but we can also see through it in order to see the shoulder joint. Finally, I caused the left arm to be rendered as a wireframe drawing instead of a solid drawing. This made it possible for us to see the center point of the left arm along with the 3D axes associated with that center point. Note the directions of the axes To begin our analysis, we recognize that the green axis is pointed up at this point. Similarly, the blue axis is pointing toward the front (from the coaches viewpoint), and the red axis is pointing into the coach's upper body toward his right side.

12 Should we move his arm? Three of the motion possibilities having to do with six degrees of freedom involve movement or translation along those axes. We can quickly recognize, however, that if we move the arm along any of those axes without causing the coach's upper body to move at the same time, we will simply rip the coach's left arm off of his body. For example, Figure 8 shows the result of moving the arm a short distance to the left along the red axis. Figure 8. Left arm moved to the left. Therefore, unless we are animating a torture chamber, the three translation possibilities available for the arm aren't very useful.

13 Rotate around the green axis Another motion possibility is to rotate the arm around the green axis. If we turn the arm onefourth of a revolution (90 degrees) to the right, the coach will be pointing to the front. That would be OK, as shown in Figure 9. Figure 9. Arm turned 90 degrees to the right. However, if we turn the arm to the left instead of the right, we can't turn it very far until we would put it in a position that is not possible for most humans. So, we would need to be careful as to the limits if we turn the arm to the right or to the left.

14 Rotate around the red axis We could turn the arm backwards so as to rotate it around the red axis by as much as one-half revolution (180 degrees) as shown in Figure 10. However, turning the arm backwards by more than this, or turning the arm forward by any amount at all would put the arm in an unnatural position. Figure 10. Arm turned backwards by 180 degrees.

15 Rotate the arm around the blue axis That leaves us with two more possibilities. We can roll the arm to the left or to the right, thus causing it to rotate around the blue axis. For example, Figure 11 shows the arm rolled to the right by one-eighth of a revolution (45 degrees). Figure 11. Arm rolled right by 45 degrees. As you can see, this caused the coach to lift his arm so as to point skyward. Difference between a right roll and a left roll The difference between a right roll and a left roll can be a little confusing. To avoid the confusion, don't think primarily in terms of what happens to the arm proper. Rather, think of what happens to the red axis. For example, a right roll around the blue axis will cause the red axis to tilt downward, just like a right roll in an airplane will cause the right wing to tilt downward. In the case of the coach's left arm, if the red axis tilts downward, then the arm proper, which protrudes in the opposite direction from the red axis will tilt upward. The grand finale It is important to note that when one of these turn or roll operations is performed, the arm's 3D axes travel or rotate with the arm. For example, the green axis no longer points straight up in Figure 11. As a result, we could follow the motion in Figure 11 by a turn to the right by 45 degrees (rotation around the new position of the green axis) and follow that by a turn backwards by 180 degrees (rotation around the new position of the red axis) resulting in the image shown in Figure 12.

16 Figure 12. Arm point to the left and up with palm up. Note that I made all of the coach's body parts visible in Figure 12 so that we can see the new position of the left arm in the context of the entire body. In this case, the coach is pointing slightly upward and slightly to his left with his palm turned up. Summary In this lesson, I explained some of the concepts surrounding an object in 3D space in general, as well as some of the Alice-specific concepts surrounding an object in 3D space. For example, I explained the concept of an Alice center point and the color coding used by Alice for each of the three axes that intersect at the center point in an Alice object. I explained the concept of yaw, pitch, and roll and related them to the methods named turn and roll in Alice programming. I explained that many of the objects in the Alice gallery are constructed from smaller component objects, and that every component object that is used to construct a larger object has its own center point and its own 3D coordinate system. I explained the meaning of the commonly used term "six degrees of freedom" and explained that every Alice object has six degrees of freedom. I also explained however, that it may not be realistic to exercise all six in a particular animation. I walked you through the fairly difficult procedure of applying motion to one of the arms belonging to a computer replica of a human while avoiding putting the arm in unnatural positions.

Chapter 2 Motion. Now consider a horizontal pipe running through it (left to right). Now, a vertical pipe (top to bottom) runs through the same point.

Chapter 2 Motion. Now consider a horizontal pipe running through it (left to right). Now, a vertical pipe (top to bottom) runs through the same point. Chapter 2 Motion Section 1 Object motion At the end of the previous chapter, you used the mouse to move objects around the screen to position them in desired locations. Some of the exercises were probably

More information

Chapter 12 Notes: Optics

Chapter 12 Notes: Optics Chapter 12 Notes: Optics How can the paths traveled by light rays be rearranged in order to form images? In this chapter we will consider just one form of electromagnetic wave: visible light. We will be

More information

Animatron Tutorial. Ronald Bourret

Animatron Tutorial. Ronald Bourret Animatron Tutorial Ronald Bourret http://www.rpbourret.com Table of Contents License... 2 Lesson 1: Getting Started... 3 1.1 Creating an Animatron account... 3 1.2 Animatron screen... 3 Lesson 2: Drawing...

More information

3.6: First Person Computer Games

3.6: First Person Computer Games 3.6: First Person Computer Games Projections of 3-D Objects Alice is an educational software program that uses a 3-D environment to teach students programming. If you have not done so already, please download

More information

Working with the BCC Z Space II Filter

Working with the BCC Z Space II Filter Working with the BCC Z Space II Filter Normally, if you create an effect with multiple DVE layers, each layer is rendered separately. The layer that is topmost in the timeline overlaps all other layers,

More information

Chapter 5. Transforming Shapes

Chapter 5. Transforming Shapes Chapter 5 Transforming Shapes It is difficult to walk through daily life without being able to see geometric transformations in your surroundings. Notice how the leaves of plants, for example, are almost

More information

The Alice Scene Editor

The Alice Scene Editor Facilitation Guide The Alice Scene Editor ( http://www.alice.org/resources/lessons/building-a-scene/ ) Summary This facilitation guide is intended to guide the instructor through the introduction of the

More information

Grade 7/8 Math Circles November 3/4, M.C. Escher and Tessellations

Grade 7/8 Math Circles November 3/4, M.C. Escher and Tessellations Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Tiling the Plane Grade 7/8 Math Circles November 3/4, 2015 M.C. Escher and Tessellations Do the following

More information

Name: Date: Concave Mirrors. 1. Reflect the rays off of the concave mirror. Principal axis

Name: Date: Concave Mirrors. 1. Reflect the rays off of the concave mirror. Principal axis Name: Date: Concave Mirrors 1. Reflect the rays off of the concave mirror. Principal axis Concave Mirrors Draw one line on each diagram to illustrate each of the following rules: a. Any ray that travels

More information

Answers. Chapter 2. 1) Give the coordinates of the following points:

Answers. Chapter 2. 1) Give the coordinates of the following points: Answers Chapter 2 1) Give the coordinates of the following points: a (-2.5, 3) b (1, 2) c (2.5, 2) d (-1, 1) e (0, 0) f (2, -0.5) g (-0.5, -1.5) h (0, -2) j (-3, -2) 1 2) List the 48 different possible

More information

Sphero Lightning Lab Cheat Sheet

Sphero Lightning Lab Cheat Sheet Actions Tool Description Variables Ranges Roll Combines heading, speed and time variables to make the robot roll. Duration Speed Heading (0 to 999999 seconds) (degrees 0-359) Set Speed Sets the speed of

More information

When you move an (unparented and unrotated) item in Layout, generally your mouse movements have the following effects:

When you move an (unparented and unrotated) item in Layout, generally your mouse movements have the following effects: Translate Group Move (default keyboard shortcut T) When you move an (unparented and unrotated) item in Layout, generally your mouse movements have the following effects: Movement Move Left/Right LMB Up/Down

More information

1. What is the law of reflection?

1. What is the law of reflection? Name: Skill Sheet 7.A The Law of Reflection The law of reflection works perfectly with light and the smooth surface of a mirror. However, you can apply this law to other situations. For example, how would

More information

THE FOURTH DIMENSION (AND MORE!)

THE FOURTH DIMENSION (AND MORE!) THE FOURTH DIMENSION (AND MORE!) The text leads us from zero dimensions (a point), to one dimension (a line), to two dimensions (a plane), to three dimensions (our familiar space), and then to four dimensions

More information

Chapter 15: Penguin - Point Editing and Blending

Chapter 15: Penguin - Point Editing and Blending This tutorial demonstrates point-editing techniques including moving and scaling control points and adding knots to surfaces to increase control. In addition, you will use blends to create smooth transitions

More information

Unit 1, Lesson 1: Tiling the Plane

Unit 1, Lesson 1: Tiling the Plane Unit 1, Lesson 1: Tiling the Plane Let s look at tiling patterns and think about area. 1.1: Which One Doesn t Belong: Tilings Which pattern doesn t belong? 1 1.2: More Red, Green, or Blue? m.openup.org//6-1-1-2

More information

Walk Cycle with Symbols

Walk Cycle with Symbols Walk Cycle with Symbols STEP 1 Assuming you have your character all rigged and ready to go, double click on the character to get into the master symbol to see all the layers that make up all of the character

More information

Working with the Dope Sheet Editor to speed up animation and reverse time.

Working with the Dope Sheet Editor to speed up animation and reverse time. Bouncing a Ball Page 1 of 2 Tutorial Bouncing a Ball A bouncing ball is a common first project for new animators. This classic example is an excellent tool for explaining basic animation processes in 3ds

More information

Using Flash Animation Basics

Using Flash Animation Basics Using Flash Contents Using Flash... 1 Animation Basics... 1 Exercise 1. Creating a Symbol... 2 Exercise 2. Working with Layers... 4 Exercise 3. Using the Timeline... 6 Exercise 4. Previewing an animation...

More information

Beaumont Middle School Design Project April May 2014 Carl Lee and Craig Schroeder

Beaumont Middle School Design Project April May 2014 Carl Lee and Craig Schroeder Beaumont Middle School Design Project April May 2014 Carl Lee and Craig Schroeder 1 2 SketchUp 1. SketchUp is free, and you can download it from the website www.sketchup.com. For some K12 use, see www.sketchup.com/3dfor/k12-education.

More information

Tutorial 4: Texture Mapping Techniques

Tutorial 4: Texture Mapping Techniques Tutorial 4: Texture Mapping Techniques Completion time 40 minutes In the previous tutorial we learned how to create materials, and how to assign texture maps to those materials. In this tutorial we will

More information

4. Refraction. glass, air, Perspex and water.

4. Refraction. glass, air, Perspex and water. Mr. C. Grima 11 1. Rays and Beams A ray of light is a narrow beam of parallel light, which can be represented by a line with an arrow on it, in diagrams. A group of rays makes up a beam of light. In laboratory

More information

BoA Tools Page 1 / 31

BoA Tools Page 1 / 31 BoA Tools Page 1 / 31 Standard tools Overview 2 Work pane 3 3D-2D file Main palette 6 Layout Main Palette 9 Navigation tools 11 Workplane Palette 14 Cursor Palette 21 Numeric control 24 Selection by Criteria

More information

Working with the BCC Z Space I Filter

Working with the BCC Z Space I Filter Working with the BCC Z Space I Filter Normally, if you create an effect with multiple DVE layers, each layer is rendered separately. The layer that is topmost in the timeline overlaps all other layers,

More information

(Refer Slide Time: 00:02:02)

(Refer Slide Time: 00:02:02) Computer Graphics Prof. Sukhendu Das Dept. of Computer Science and Engineering Indian Institute of Technology, Madras Lecture - 20 Clipping: Lines and Polygons Hello and welcome everybody to the lecture

More information

Modeling a Gear Standard Tools, Surface Tools Solid Tool View, Trackball, Show-Hide Snaps Window 1-1

Modeling a Gear Standard Tools, Surface Tools Solid Tool View, Trackball, Show-Hide Snaps Window 1-1 Modeling a Gear This tutorial describes how to create a toothed gear. It combines using wireframe, solid, and surface modeling together to create a part. The model was created in standard units. To begin,

More information

Topic. Section 4.1 (3, 4)

Topic. Section 4.1 (3, 4) Topic.. California Standards: 6.0: Students graph a linear equation and compute the x- and y-intercepts (e.g., graph x + 6y = ). They are also able to sketch the region defined by linear inequality (e.g.,

More information

Installing and Using Trackside Cameras Revised November 2008

Installing and Using Trackside Cameras Revised November 2008 Installing and Using Trackside Cameras Revised November 2008 Trackside cameras are a useful and creative way to add visual interest to your route. Rather than just look out the windshield of the locomotive

More information

Physics Optics Problems. Science and Mathematics Education Research Group

Physics Optics Problems. Science and Mathematics Education Research Group F FA ACULTY C U L T Y OF O F EDUCATION E D U C A T I O N Department of Curriculum and Pedagogy Physics Optics Problems Science and Mathematics Education Research Group Supported by UBC Teaching and Learning

More information

This document describes the user interface, navigation and the common resources that are available in SvalSim

This document describes the user interface, navigation and the common resources that are available in SvalSim Page 1 Geo2000 SvalSim Documentation This documentation will help you to discover and use the SvalSim geosimulator. It will tell you in general how the simulator works and how to use it. General information

More information

WJEC MATHEMATICS INTERMEDIATE GRAPHS STRAIGHT LINE GRAPHS (PLOTTING)

WJEC MATHEMATICS INTERMEDIATE GRAPHS STRAIGHT LINE GRAPHS (PLOTTING) WJEC MATHEMATICS INTERMEDIATE GRAPHS STRAIGHT LINE GRAPHS (PLOTTING) 1 Contents Some Simple Straight Lines y = mx + c Parallel Lines Perpendicular Lines Plotting Equations Shaded Regions Credits WJEC Question

More information

Web-Friendly Sites. Planning & Design 1

Web-Friendly Sites. Planning & Design 1 Planning & Design 1 This tutorial presents useful tips and tricks to help you achieve a more Web-friendly design and make your sites more efficient. The following topics are discussed: How Z-order and

More information

Tangents. In this tutorial we are going to take a look at how tangents can affect an animation.

Tangents. In this tutorial we are going to take a look at how tangents can affect an animation. Tangents In this tutorial we are going to take a look at how tangents can affect an animation. One of the 12 Principles of Animation is called Slow In and Slow Out. This refers to the spacing of the in

More information

ILLUSTRATOR TUTORIAL-1 workshop handout

ILLUSTRATOR TUTORIAL-1 workshop handout Why is Illustrator a powerful tool? ILLUSTRATOR TUTORIAL-1 workshop handout Computer graphics fall into two main categories, bitmap graphics and vector graphics. Adobe Illustrator is a vector based software

More information

Stop-Motion TOPICS. The Stop-Motion Camera Stop-Motion Options Add Mode Stop-Motion Camera Orientation Onion Skin

Stop-Motion TOPICS. The Stop-Motion Camera Stop-Motion Options Add Mode Stop-Motion Camera Orientation Onion Skin Stop-Motion Stop-Motion is a technique whereby objects are photographed in a series of slightly different positions such that they appear to move when the photographs are played back in quick succession.

More information

Part II: Creating Visio Drawings

Part II: Creating Visio Drawings 128 Part II: Creating Visio Drawings Figure 5-3: Use any of five alignment styles where appropriate. Figure 5-4: Vertical alignment places your text at the top, bottom, or middle of a text block. You could

More information

BCC Sphere Transition

BCC Sphere Transition BCC Sphere Transition The Sphere Transition shape models the source image onto a sphere. Unlike the Sphere filter, the Sphere Transition filter allows you to animate Perspective, which is useful in creating

More information

Science 8 Chapter 5 Section 1

Science 8 Chapter 5 Section 1 Science 8 Chapter 5 Section 1 The Ray Model of Light (pp. 172-187) Models of Light wave model of light: a model in which light is a type of wave that travels through space and transfers energy from one

More information

Adding Depth to Games

Adding Depth to Games Game Maker Tutorial Adding Depth to Games Written by Mark Overmars Copyright 2007-2009 YoYo Games Ltd Last changed: December 23, 2009 Uses: Game Maker 8.0, Pro Edition, Advanced Mode Level: Intermediate

More information

Pong in Unity a basic Intro

Pong in Unity a basic Intro This tutorial recreates the classic game Pong, for those unfamiliar with the game, shame on you what have you been doing, living under a rock?! Go google it. Go on. For those that now know the game, this

More information

Rational Numbers and the Coordinate Plane

Rational Numbers and the Coordinate Plane Rational Numbers and the Coordinate Plane LAUNCH (8 MIN) Before How can you use the numbers placed on the grid to figure out the scale that is used? Can you tell what the signs of the x- and y-coordinates

More information

Telling a Story Visually. Copyright 2012, Oracle. All rights reserved.

Telling a Story Visually. Copyright 2012, Oracle. All rights reserved. What Will I Learn? Objectives In this lesson, you will learn how to: Compare and define an animation and a scenario Demonstrate how to use the four problem solving steps to storyboard your animation Use

More information

SketchUp Starting Up The first thing you must do is select a template.

SketchUp Starting Up The first thing you must do is select a template. SketchUp Starting Up The first thing you must do is select a template. While there are many different ones to choose from the only real difference in them is that some have a coloured floor and a horizon

More information

Advances in MicroStation 3D

Advances in MicroStation 3D MW1HC515 Advances in MicroStation 3D Hands-on class sponsored by the Bentley Institute Presenter: Sam Hendrick, Senior MicroStation Product Consultant Bentley Systems, Incorporated 685 Stockton Drive Exton,

More information

Physics for Scientists & Engineers 2

Physics for Scientists & Engineers 2 Geometric Optics Physics for Scientists & Engineers 2 Spring Semester 2005 Lecture 36! The study of light divides itself into three fields geometric optics wave optics quantum optics! In the previous chapter,

More information

Geometric Transformations

Geometric Transformations Geometric Transformations CS 4620 Lecture 9 2017 Steve Marschner 1 A little quick math background Notation for sets, functions, mappings Linear and affine transformations Matrices Matrix-vector multiplication

More information

Lecture 3 Sections 2.2, 4.4. Mon, Aug 31, 2009

Lecture 3 Sections 2.2, 4.4. Mon, Aug 31, 2009 Model s Lecture 3 Sections 2.2, 4.4 World s Eye s Clip s s s Window s Hampden-Sydney College Mon, Aug 31, 2009 Outline Model s World s Eye s Clip s s s Window s 1 2 3 Model s World s Eye s Clip s s s Window

More information

1.! Questions about reflected intensity. [Use the formulas on p. 8 of Light.] , no matter

1.! Questions about reflected intensity. [Use the formulas on p. 8 of Light.] , no matter Reading: Light Key concepts: Huygens s principle; reflection; refraction; reflectivity; total reflection; Brewster angle; polarization by absorption, reflection and Rayleigh scattering. 1.! Questions about

More information

lundi 7 janvier 2002 Blender: tutorial: Building a Castle Page: 1

lundi 7 janvier 2002 Blender: tutorial: Building a Castle Page: 1 lundi 7 janvier 2002 Blender: tutorial: Building a Castle Page: 1 www.blender.nl this document is online at http://www.blender.nl/showitem.php?id=4 Building a Castle 2000 07 19 Bart Veldhuizen id4 Introduction

More information

What s New to Version 2.0

What s New to Version 2.0 SU Animate 2.0 Guide What s New to Version 2.0...1 Install...2 Cameras, Curves & Paths...3 Use a Camera path to create a simple walk thru effect...8 Animating Objects with Target Groups...9 Using four

More information

Autodesk Navisworks Freedom Quick Reference Guide

Autodesk Navisworks Freedom Quick Reference Guide WP CAD 00074 March 2012 Guide by Andy Davis Autodesk Navisworks Freedom Quick Reference Guide Quick Reference Guide to Autodesk Navisworks Freedom Opening a Model To open a model, click on the Application

More information

Answer Key: Three-Dimensional Cross Sections

Answer Key: Three-Dimensional Cross Sections Geometry A Unit Answer Key: Three-Dimensional Cross Sections Name Date Objectives In this lesson, you will: visualize three-dimensional objects from different perspectives be able to create a projection

More information

A bouncing ball squashes on its vertical axis and stretches on the horizontal axis as it strikes the ground.

A bouncing ball squashes on its vertical axis and stretches on the horizontal axis as it strikes the ground. Animation Principles The following 12 animation principles are those distilled from the combined wisdom of animators over several decades. Animators developed their own techniques in animating characters,

More information

The Wireframe Update Buttons. The Frontface and Backface Buttons. The Project Designer 265

The Wireframe Update Buttons. The Frontface and Backface Buttons. The Project Designer 265 The Wireframe Update Buttons The speed at which objects can be manipulated in the Project Designer viewport depends in part on the complexity of the object being moved. An object that is made up of many

More information

Name Class Date. Using Graphs to Relate Two Quantities

Name Class Date. Using Graphs to Relate Two Quantities 4-1 Reteaching Using Graphs to Relate Two Quantities An important life skill is to be able to a read graph. When looking at a graph, you should check the title, the labels on the axes, and the general

More information

Lesson 11. Polygonal Spaceship

Lesson 11. Polygonal Spaceship 11 Polygonal Spaceship In this lesson, you will build and texture map a polygonal spaceship. Starting with a polygonal cube, you will extrude facets until you have a completed ship. You will then be able

More information

Three-Dimensional Figures

Three-Dimensional Figures Three-Dimensional Figures The number of coins created by the U.S. Mint changes each year. In the year 2000, there were about 28 billion coins created and about half of them were pennies!.1 Whirlygigs for

More information

Design and Development of Unmanned Tilt T-Tri Rotor Aerial Vehicle

Design and Development of Unmanned Tilt T-Tri Rotor Aerial Vehicle Design and Development of Unmanned Tilt T-Tri Rotor Aerial Vehicle K. Senthil Kumar, Mohammad Rasheed, and T.Anand Abstract Helicopter offers the capability of hover, slow forward movement, vertical take-off

More information

Mathematics 308 Geometry. Chapter 9. Drawing three dimensional objects

Mathematics 308 Geometry. Chapter 9. Drawing three dimensional objects Mathematics 308 Geometry Chapter 9. Drawing three dimensional objects In this chapter we will see how to draw three dimensional objects with PostScript. The task will be made easier by a package of routines

More information

Two-Dimensional Waves

Two-Dimensional Waves Two-Dimensional Waves In our previous lessons, we discussed one-dimensional waves waves that can only travel in straight lines, such as along the length of a spring. In this next part of the unit, we will

More information

Taking the Best Reference Photos

Taking the Best Reference Photos Sides Three and Four To fill in the other two sides select the top vertice and the corners on a side where there is no face yet. Again, use FKEY to fill in a face. Repeat this for the last side to have

More information

Computer Science 474 Spring 2010 Viewing Transformation

Computer Science 474 Spring 2010 Viewing Transformation Viewing Transformation Previous readings have described how to transform objects from one position and orientation to another. One application for such transformations is to create complex models from

More information

Practice Exam Sample Solutions

Practice Exam Sample Solutions CS 675 Computer Vision Instructor: Marc Pomplun Practice Exam Sample Solutions Note that in the actual exam, no calculators, no books, and no notes allowed. Question 1: out of points Question 2: out of

More information

Adobe Flash CS4 Part 4: Interactivity

Adobe Flash CS4 Part 4: Interactivity CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES Adobe Flash CS4 Part 4: Interactivity Fall 2010, Version 1.0 Table of Contents Introduction... 2 Downloading the Data Files... 2

More information

This overview summarizes topics described in detail later in this chapter.

This overview summarizes topics described in detail later in this chapter. 20 Application Environment: Robot Space and Motion Overview This overview summarizes topics described in detail later in this chapter. Describing Space A coordinate system is a way to describe the space

More information

Just change the sign of the -coordinate. Let s look at the triangle from our previous example and reflect

Just change the sign of the -coordinate. Let s look at the triangle from our previous example and reflect . onstructing Reflections Now we begin to look at transformations that yield congruent images. We ll begin with reflections and then move into a series of transformations. series of transformations applies

More information

The playhead, shown as a vertical red beam, passes each frame when a movie plays back, much like movie fi lm passing in front of a projector bulb.

The playhead, shown as a vertical red beam, passes each frame when a movie plays back, much like movie fi lm passing in front of a projector bulb. The project: AIRPLANE I will show you a completed version of this project.. Introducing keyframes and the Timeline One of the most important panels in the Flash workspace is the Timeline, which is where

More information

Interesting Application. Linear Algebra

Interesting Application. Linear Algebra MATH 308A PROJECT: An Interesting Application of Linear Algebra Produced by: Kristen Pilawski Math 308 A Professor James King Fall 2001 Application: Space Shuttle Control Systems Abstract: This report

More information

AutoCAD 2009 Tutorial

AutoCAD 2009 Tutorial AutoCAD 2009 Tutorial Second Level: 3D Modeling Randy H. Shih Oregon Institute of Technology SDC PUBLICATIONS Schroff Development Corporation www.schroff.com Better Textbooks. Lower Prices. AutoCAD 2009

More information

CSIS 0801 Final Year Project. Implementation of An Intelligent Hexapod Robot. Individual Final Report - Kinematics

CSIS 0801 Final Year Project. Implementation of An Intelligent Hexapod Robot. Individual Final Report - Kinematics CSIS 0801 Final Year Project Implementation of An Intelligent Hexapod Robot Individual Final Report - Kinematics FYP Account: fyp14013 Name: Yip Sit Wun (Terry) UID: 3035009744 HKU CS FYP14013 Implementation

More information

A simple problem that has a solution that is far deeper than expected!

A simple problem that has a solution that is far deeper than expected! The Water, Gas, Electricity Problem A simple problem that has a solution that is far deeper than expected! Consider the diagram below of three houses and three utilities: water, gas, and electricity. Each

More information

Homework Set 3 Due Thursday, 07/14

Homework Set 3 Due Thursday, 07/14 Homework Set 3 Due Thursday, 07/14 Problem 1 A room contains two parallel wall mirrors, on opposite walls 5 meters apart. The mirrors are 8 meters long. Suppose that one person stands in a doorway, in

More information

AREA Judo Math Inc.

AREA Judo Math Inc. AREA 2013 Judo Math Inc. 6 th grade Problem Solving Discipline: Black Belt Training Order of Mastery: Area 1. Area of triangles by composition 2. Area of quadrilaterals by decomposing 3. Draw polygons

More information

Chapter 15. Light Waves

Chapter 15. Light Waves Chapter 15 Light Waves Chapter 15 is finished, but is not in camera-ready format. All diagrams are missing, but here are some excerpts from the text with omissions indicated by... After 15.1, read 15.2

More information

Create Models or Use a Library? Create your own library How to Get Started? [ 140 ]

Create Models or Use a Library? Create your own library How to Get Started? [ 140 ] The next step for our scenes is to add some furniture, to further increase the realism. As furniture is a key element, every item of furniture that we add to the scene increases the level of detail, and

More information

Light and the Properties of Reflection & Refraction

Light and the Properties of Reflection & Refraction Light and the Properties of Reflection & Refraction OBJECTIVE To study the imaging properties of a plane mirror. To prove the law of reflection from the previous imaging study. To study the refraction

More information

Optics INTRODUCTION DISCUSSION OF PRINCIPLES. Reflection by a Plane Mirror

Optics INTRODUCTION DISCUSSION OF PRINCIPLES. Reflection by a Plane Mirror Optics INTRODUCTION Geometric optics is one of the oldest branches of physics, dealing with the laws of reflection and refraction. Reflection takes place on the surface of an object, and refraction occurs

More information

Chapter 0. Getting Started. Objectives

Chapter 0. Getting Started. Objectives Chapter 0 Getting Started Objectives Install the Java editor Install the Alice environment Setup the Java editor to work with the Alice environment Explain the purpose of Alice Setup an Alice scene Installing

More information

Autodesk Moldflow Insight AMI User Interface

Autodesk Moldflow Insight AMI User Interface Autodesk Moldflow Insight 2012 AMI User Interface Revision 1, 18 March 2012. This document contains Autodesk and third-party software license agreements/notices and/or additional terms and conditions for

More information

Mathematics Background

Mathematics Background Finding Area and Distance Students work in this Unit develops a fundamentally important relationship connecting geometry and algebra: the Pythagorean Theorem. The presentation of ideas in the Unit reflects

More information

LESSON 2 MODELING BASICS

LESSON 2 MODELING BASICS LESSON 2 MODELING BASICS In this lesson we ll start to model a multi-story office building from scratch. We ll construct the base grid, create the two towers and place slabs between the stories. Also we

More information

26 Geometric Optics, Reflection

26 Geometric Optics, Reflection 26 Geometric Optics, Reflection We now turn to a branch of optics referred to as geometric optics and also referred to as ray optics. It applies in cases where the dimensions of the objects (and apertures)

More information

Alice. Coverage. Mathematical Expressions, Conditional Statements, Control Structures. Arithmetic Expressions Built-in Functions Conditional Execution

Alice. Coverage. Mathematical Expressions, Conditional Statements, Control Structures. Arithmetic Expressions Built-in Functions Conditional Execution Alice Mathematical Expressions, Conditional Statements, Control Structures Coverage Arithmetic Expressions Built-in Functions Conditional Execution If/Then Statements Control Structures Loops 1 Functions

More information

Polygons in the Coordinate Plane

Polygons in the Coordinate Plane Polygons in the Coordinate Plane LAUNCH (8 MIN) Before How can you find the perimeter of the sandbox that the park worker made? During How will you determine whether the park worker s plan for the sandbox

More information

Objective: Construct a coordinate system on a plane.

Objective: Construct a coordinate system on a plane. Lesson 2 Objective: Construct a coordinate system on a plane. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (10 minutes) (7 minutes) (33

More information

1. Mesh Coloring a.) Assign unique color to each polygon based on the polygon id.

1. Mesh Coloring a.) Assign unique color to each polygon based on the polygon id. 1. Mesh Coloring a.) Assign unique color to each polygon based on the polygon id. Figure 1: The dragon model is shown rendered using a coloring scheme based on coloring each triangle face according to

More information

5 Subdivision Surfaces

5 Subdivision Surfaces 5 Subdivision Surfaces In Maya, subdivision surfaces possess characteristics of both polygon and NURBS surface types. This hybrid surface type offers some features not offered by the other surface types.

More information

CS 465 Program 4: Modeller

CS 465 Program 4: Modeller CS 465 Program 4: Modeller out: 30 October 2004 due: 16 November 2004 1 Introduction In this assignment you will work on a simple 3D modelling system that uses simple primitives and curved surfaces organized

More information

B ABC is mapped into A'B'C'

B ABC is mapped into A'B'C' h. 00 Transformations Sec. 1 Mappings & ongruence Mappings Moving a figure around a plane is called mapping. In the figure below, was moved (mapped) to a new position in the plane and the new triangle

More information

Section 1.5 Transformation of Functions

Section 1.5 Transformation of Functions 6 Chapter 1 Section 1.5 Transformation of Functions Often when given a problem, we try to model the scenario using mathematics in the form of words, tables, graphs and equations in order to explain or

More information

Quick Crash Scene Tutorial

Quick Crash Scene Tutorial Quick Crash Scene Tutorial With Crash Zone or Crime Zone, even new users can create a quick crash scene diagram in less than 10 minutes! In this tutorial we ll show how to use Crash Zone s unique features

More information

Camera Shots. Lesson Plan

Camera Shots. Lesson Plan Lesson Plan Camera Shots Level: Grades 9-12 About the Author With permission, this lesson is based on a series of activities by Wayne McNanney in Mediacy, Vol. 20, No. 3, Fall 1998, and from TVOntario's

More information

Chapter Adding 1- T Mo he tio B n le to nde Yo r ur Inte Scerfac ne e Landscape Scene Stormy Night.mp4 End 200 Default Animation frame 1 Location

Chapter Adding 1- T Mo he tio B n le to nde Yo r ur Inte Scerfac ne e Landscape Scene Stormy Night.mp4 End 200 Default Animation frame 1 Location 1- The Blender Interface Adding Motion to Your Scene Open your Landscape Scene file and go to your scene buttons. It s time to animate our dark and stormy night. We will start by making the correct setting

More information

Index of Refraction and Total Internal Reflection

Index of Refraction and Total Internal Reflection Index of Refraction and Total Internal Reflection Name: Group Members: Date: TA s Name: Materials: Ray box, two different transparent blocks, two letter size white pages, pencil, protractor, two nails,

More information

Velocity: A Bat s Eye View of Velocity

Velocity: A Bat s Eye View of Velocity Name School Date Purpose Velocity: A Bat s Eye View of Velocity There are a number of ways of representing motion that we ll find useful. Graphing position, velocity, and acceleration vs. time is often

More information

In our first lecture on sets and set theory, we introduced a bunch of new symbols and terminology.

In our first lecture on sets and set theory, we introduced a bunch of new symbols and terminology. Guide to and Hi everybody! In our first lecture on sets and set theory, we introduced a bunch of new symbols and terminology. This guide focuses on two of those symbols: and. These symbols represent concepts

More information

Viewing with Computers (OpenGL)

Viewing with Computers (OpenGL) We can now return to three-dimension?', graphics from a computer perspective. Because viewing in computer graphics is based on the synthetic-camera model, we should be able to construct any of the classical

More information

Animatron Tutorial. Ronald Bourret

Animatron Tutorial. Ronald Bourret Animatron Tutorial Ronald Bourret http://www.rpbourret.com Table of Contents License... 2 Lesson 1: Getting Started... 3 1.1 Create an Animatron Account... 3 1.2 Animatron Screen... 3 Lesson 2: Drawing...

More information

Section 3.1 Graphing Using the Rectangular Coordinate System

Section 3.1 Graphing Using the Rectangular Coordinate System Objectives Section 3.1 Graphing Using the Rectangular Coordinate System n Construct a rectangular coordinate system n Plot ordered pairs and determine the coordinates of a point n Graph paired data n Read

More information

Introduction. There are two basic ways to apply more than one texture to one object:

Introduction. There are two basic ways to apply more than one texture to one object: Introduction For recent versions of Trainz, gmax will not handle the standards for new material types and options such as Specular and Bump or Normal mapping. The Trainz forum has published techniques

More information