Alternative Designs Report 3D Ultrasound Reconstruction By: Michael Golden Khayriyyah Munir Omid Nasser Bidgeli. Team #3. Client: Dr.

Size: px
Start display at page:

Download "Alternative Designs Report 3D Ultrasound Reconstruction By: Michael Golden Khayriyyah Munir Omid Nasser Bidgeli. Team #3. Client: Dr."

Transcription

1 Alternative Designs Report 3D Ultrasound Reconstruction By: Michael Golden Khayriyyah Munir Omid Nasser Bidgeli Team #3 Client: Dr. Joseph McIsaac

2 Alternative Design 1- Camera Mounting Two cameras will be mounted on 80/20 Inc s T-slotted aluminum framing in a constructed mounting mold. There are three options for the setup of the mount. Option 1 Fixed sawhorse support In this design, there are a total of five bars, all composed of 80/20 Inc s T-slotted aluminum. Bar A is four feet long and arranged parallel to the floor with both cameras mounted parallel to each other. The cameras are mobile in the x-direction in order to find an optimal distance between them for more accurate determinations of the distance between the cameras and the patient. Bars B and Bars C are also four feet long and are connected at 30 degrees. All bars are connected at points P and Q. The advantages of this design include the mobility of the cameras in the x direction as well as the convenience of the support structure. With everything connected, the structure can be taken from room to room to be used wherever needed.

3 Option 2- Sliding angled support In this design, there are a total of five bars, all composed of 80/20 Inc s T-slotted aluminum. Bar A is four feet long and arranged parallel to the floor, with two cameras mounted parallel to each other. The cameras are mobile in the x-direction in order to find the optimal distance between them for more accurate determinations of the distance between the cameras and the patient. Bar A is attached at either end to Bars B, and is mobile in the plane of Bars B. Bars B are each fixed to a two foot Bar C at 60 degrees. The advantages of this design include the ability for the cameras to move in the y-direction. This allows the physician to adjust the height of the cameras to be specific for any bed or patient in the hospital. The disadvantages of this design include the fact that as the height of Bar A decreases, the angle between the cameras and what needs to be imaged on the patient changes. This significantly increases the mathematical calculations necessary to determine the position of the ultrasound probe because a new set of calculations is necessary for every location of Bar A.

4 Option 3 Sliding perpendicular support In this design, there are a total of five bars, all composed of 80/20 Inc s T-slotted aluminum. Bar A is four feet long and arranged parallel to the floor, with two cameras mounted parallel to each other. The cameras are mobile in the x-direction in order to find an optimal distance between them for more accurate determinations of the distance between the cameras and the patient. Bars B are perpendicular to the floor, and each attached to either end of Bar A. Bar A is mobile in the y-direction because Bar A is composed of T-slotted aluminum. The advantages of this design include the ability for the cameras to move in both the x-direction and the y-direction, making it possible to find the optimal position for both cameras for various bed heights throughout the hospital and patient sizes.

5 Alternative Design 2 Camera Configuration Option 1 Perpendicular In this design, each camera will be mounted to one end of an L-shaped support with each leg measuring 4.5 feet in length. They will both image the probe and tracking system, but in a perpendicular fashion. The disadvantages of this design include the fact that is very bulky and requires a lot of material. It takes up a lot of space and would inhibit the movement of the physician, and therefore his contact with the patient, from two directions. Also with the cameras arranged 90 degrees to each other, the convergence of the image areas is much less, so the location of the patient needs to be very specific and is not easily changed with patient variance.

6 Option 2 Parallel In this design, both cameras are arranged on one bar, four feet in length, and parallel to each other. Because they both image from the same direction, the stereotriangulation calculations are simpler. The cameras are close to each other which makes this design extremely space efficient. The optimal distance from the patient is four feet, and as along as this is the case the spatial configuration can be anything, as long as the patient is in the view of the cameras. There is no need for the cameras to be in any one specific location, which is desirable for the physician.

7 Alternative Design 3 Tracking system configuration Option 1 In-line Configuration In this design, spheres A, B, and D are configured in an equilateral triangle, all in the same plane. The ultrasound probe is attached to sphere A, in the same line as that made by connected A and B. The disadvantages of this design include the fact that if for some reason the ultrasound probe is in line with the focal line of one of the cameras, the camera will only image two spheres, with the other being lost. This would give rise to complications in the calculations, as information from three spheres is necessary for sterotraingulation.

8 Option 2 Perpendicular and off Center In this design, spheres A, B, and D are configured in an equilateral triangle, all in the same plane. The ultrasound probe is attached to sphere D, perpendicular to the plane formed by spheres A, B, and D. The advantages to this design include that at any point all three spheres are imaged, and there is no way for them to block one another from either one of the cameras. Disadvantages of this design include a non-optimal range of motion, particularly with respect to spheres A and B. As the angle between the probe and the neck region decreases, spheres A and B get significantly closer to the patient and can eventually make contact with the patient, limiting the range of motion in that direction.

9 Option 2 Perpendicular and Centered In this design, spheres A, B, and D are configured in an equilateral triangle, all in the same plane. The ultrasound probe is perpendicular to the plane, but at the centroid of the plane. Advantages to this design include that at any point, all three spheres are imaged and there is no way for them to block one another from either of the cameras. Also, with the ultrasound probe being located at the centroid, the physician has the greatest range of motion in any direction.

3D Ultrasound Reconstruction By The 3 Cons: Michael Golden Khayriyyah Munir Omid Nasser Bigdeli

3D Ultrasound Reconstruction By The 3 Cons: Michael Golden Khayriyyah Munir Omid Nasser Bigdeli 3D Ultrasound Reconstruction By The 3 Cons: Michael Golden Khayriyyah Munir Omid Nasser Bigdeli Client Contact: Dr. Joseph McIsaac Hartford Hospital 80 Seymour St. PO Box 5037 Hartford, CT 06102 (860)

More information

Aim: How do we find the volume of a figure with a given base? Get Ready: The region R is bounded by the curves. y = x 2 + 1

Aim: How do we find the volume of a figure with a given base? Get Ready: The region R is bounded by the curves. y = x 2 + 1 Get Ready: The region R is bounded by the curves y = x 2 + 1 y = x + 3. a. Find the area of region R. b. The region R is revolved around the horizontal line y = 1. Find the volume of the solid formed.

More information

Appendix. Software Considerations, Design, and Technique Used

Appendix. Software Considerations, Design, and Technique Used Page 1 Appendix Technique Validation This study used the principles of stereophotogrammetry to measure the operative orientation of the cup for each task. Photogrammetry provides a method of obtaining

More information

Data Fusion Virtual Surgery Medical Virtual Reality Team. Endo-Robot. Database Functional. Database

Data Fusion Virtual Surgery Medical Virtual Reality Team. Endo-Robot. Database Functional. Database 2017 29 6 16 GITI 3D From 3D to 4D imaging Data Fusion Virtual Surgery Medical Virtual Reality Team Morphological Database Functional Database Endo-Robot High Dimensional Database Team Tele-surgery Robotic

More information

APS Sixth Grade Math District Benchmark Assessment NM Math Standards Alignment

APS Sixth Grade Math District Benchmark Assessment NM Math Standards Alignment SIXTH GRADE NM STANDARDS Strand: NUMBER AND OPERATIONS Standard: Students will understand numerical concepts and mathematical operations. 5-8 Benchmark N.: Understand numbers, ways of representing numbers,

More information

Mensuration: Basic Concepts and Important Formulas

Mensuration: Basic Concepts and Important Formulas Equilateral Triangle: All the three sides are equal and each angle is equal to. Height (Altitude) = 3(side) Isosceles Triangle: Two sides and two angles are equal and altitude drawn on nonequal side bisects

More information

5th Grade Mathematics Essential Standards

5th Grade Mathematics Essential Standards Standard 1 Number Sense (10-20% of ISTEP/Acuity) Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions, and percents. They understand the

More information

Area. Angle where two rays. Acute angle. Addend. a number to be added. an angle measuring less than 90 degrees. or line segments share an endpoint

Area. Angle where two rays. Acute angle. Addend. a number to be added. an angle measuring less than 90 degrees. or line segments share an endpoint Acute angle Addend an angle measuring less than 90 degrees a number to be added Angle where two rays or line segments share an endpoint Area the measure of space inside a figure. Area is measured in square

More information

Archdiocese of Washington Catholic Schools Academic Standards Mathematics

Archdiocese of Washington Catholic Schools Academic Standards Mathematics 5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,

More information

PARCC Geometry Practice Test Released April,

PARCC Geometry Practice Test Released April, Non-Calculator Part 1. The figure shows with side lengths as indicated. Enter your answer in the box. 2. The figure shows two perpendicular lines s and r intersecting at point P in the interior of a trapezoid.

More information

3. Draw the orthographic projection (front, right, and top) for the following solid. Also, state how many cubic units the volume is.

3. Draw the orthographic projection (front, right, and top) for the following solid. Also, state how many cubic units the volume is. PAP Geometry Unit 7 Review Name: Leave your answers as exact answers unless otherwise specified. 1. Describe the cross sections made by the intersection of the plane and the solids. Determine if the shape

More information

Movement analysis with SkillSpector. Version 1.0 Last update: 14/

Movement analysis with SkillSpector. Version 1.0 Last update: 14/ Movement analysis with SkillSpector Version 1.0 Last update: 14/05-2008 What is SkillSpector SkillSpector is a software program for video based movement analysis. The following analysis are available:

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

Perspective projection. A. Mantegna, Martyrdom of St. Christopher, c. 1450

Perspective projection. A. Mantegna, Martyrdom of St. Christopher, c. 1450 Perspective projection A. Mantegna, Martyrdom of St. Christopher, c. 1450 Overview of next two lectures The pinhole projection model Qualitative properties Perspective projection matrix Cameras with lenses

More information

Perimeter and Area. Slide 1 / 183. Slide 2 / 183. Slide 3 / 183. Table of Contents. New Jersey Center for Teaching and Learning

Perimeter and Area. Slide 1 / 183. Slide 2 / 183. Slide 3 / 183. Table of Contents. New Jersey Center for Teaching and Learning New Jersey Center for Teaching and Learning Slide 1 / 183 Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students

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

Finding Perimeters and Areas of Regular Polygons

Finding Perimeters and Areas of Regular Polygons Finding Perimeters and Areas of Regular Polygons Center of a Regular Polygon - A point within the polygon that is equidistant from all vertices. Central Angle of a Regular Polygon - The angle whose vertex

More information

Identifying and Classifying Angles and Shapes

Identifying and Classifying Angles and Shapes Grade 5 Mathematics, Quarter 2, Unit 2.1 Identifying and Classifying Angles and Shapes Overview Number of instructional days: 10 (1 day = 45 minutes) Content to be learned Describe, compare, and classify

More information

Mathematics Curriculum

Mathematics Curriculum 6 G R A D E Mathematics Curriculum GRADE 6 5 Table of Contents 1... 1 Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)... 11 Lesson 1: The Area of Parallelograms Through Rectangle Facts...

More information

The area of this square is 9 square units. This array has 2 rows and 5 columns. So, 2 5 = 10. The gas container has a capacity of 5 gallons.

The area of this square is 9 square units. This array has 2 rows and 5 columns. So, 2 5 = 10. The gas container has a capacity of 5 gallons. Third Grade 434 Area: The number of nonoverlapping units that cover a closed boundary (measured in square units). Array: An arrangement of objects in a regular pattern, usually rows and columns. Arrays

More information

Distance in Coordinate Geometry

Distance in Coordinate Geometry Page 1 of 6 L E S S O N 9.5 We talk too much; we should talk less and draw more. Distance in Coordinate Geometry Viki is standing on the corner of Seventh Street and 8th Avenue, and her brother Scott is

More information

10 Perimeter and Area

10 Perimeter and Area CHAPTER 10 Perimeter and Area Chapter Outline 10.1 TRIANGLES AND PARALLELOGRAMS 10.2 TRAPEZOIDS, RHOMBI, AND KITES 10.3 AREAS OF SIMILAR POLYGONS 10.4 CIRCUMFERENCE AND ARC LENGTH 10.5 AREAS OF CIRCLES

More information

2. A circle is inscribed in a square of diagonal length 12 inches. What is the area of the circle?

2. A circle is inscribed in a square of diagonal length 12 inches. What is the area of the circle? March 24, 2011 1. When a square is cut into two congruent rectangles, each has a perimeter of P feet. When the square is cut into three congruent rectangles, each has a perimeter of P 6 feet. Determine

More information

Nearing Convergence: An Interactive Set Design for Dance The Intersection of Physical Movement and Optical Form

Nearing Convergence: An Interactive Set Design for Dance The Intersection of Physical Movement and Optical Form BRIDGES Mathematical Connections in Art, Music, and Science Nearing Convergence: An Interactive Set Design for Dance The Intersection of Physical Movement and Optical Form Benigna Chill a Department of

More information

Augmenting Reality with Projected Interactive Displays

Augmenting Reality with Projected Interactive Displays Augmenting Reality with Projected Interactive Displays Claudio Pinhanez IBM T.J. Watson Research Center, P.O. Box 218 Yorktown Heights, N.Y. 10598, USA Abstract. This paper examines a steerable projection

More information

Practice. Area of Irregular Figures. Estimate the area of each figure. Each square represents 1 square foot. Choose the letter for the best answer. 1.

Practice. Area of Irregular Figures. Estimate the area of each figure. Each square represents 1 square foot. Choose the letter for the best answer. 1. Name Date Class Practice Estimate the area of each figure. Each square represents 1 square foot. Choose the letter for the best answer. 1. 2. A 11 ft 2 C 15 ft 2 B 14 ft 2 A 24 ft 2 C 32 ft 2 B 26 ft 2

More information

Similar Triangles. Triangles are similar if corresponding angles are equal. Now take a look at the sides of the two triangles shown in Figure 3.

Similar Triangles. Triangles are similar if corresponding angles are equal. Now take a look at the sides of the two triangles shown in Figure 3. Imagine you are having a picnic at the lake. You look out across the lake and see a sailboat off in the distance the sail is a tiny triangle to the naked eye. For a closer look, you pick up the binoculars

More information

Polygons. 5 sides 5 angles. pentagon. no no R89. Name

Polygons. 5 sides 5 angles. pentagon. no no R89. Name Lesson 11.1 Polygons A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. You can classify a polygon by the number of sides and the number of angles

More information

John Edwards, Virtu designer says Virtu has many attributes, but our primary goal was to create meeting rooms that would truly stimulate people.

John Edwards, Virtu designer says Virtu has many attributes, but our primary goal was to create meeting rooms that would truly stimulate people. VIRTU CONFERENCING John Edwards, Virtu designer says Virtu has many attributes, but our primary goal was to create meeting rooms that would truly stimulate people. Many of the unique elements of Virtu

More information

Standard 2.0 Knowledge of Geometry: Students will apply the properties of one-,

Standard 2.0 Knowledge of Geometry: Students will apply the properties of one-, VSC - Mathematics Print pages on legal paper, landscape mode. Grade PK Grade K Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Geometry: Students will apply the properties of one-, two-,

More information

UNIT - V PERSPECTIVE PROJECTION OF SIMPLE SOLIDS

UNIT - V PERSPECTIVE PROJECTION OF SIMPLE SOLIDS UNIT - V PERSPECTIVE PROJECTION OF SIMPLE SOLIDS Definitions 1. Perspective Projection is the graphic representation of an object on a single plane called Picture Plane (PP), as it appears to an observer.

More information

Let s Get This Started!

Let s Get This Started! Lesson. Skills Practice Name Date Let s Get This Started! Points, Lines, Planes, Rays, and Line Segments Vocabulary Write the term that best completes each statement.. A geometric figure created without

More information

Number/Computation. addend Any number being added. digit Any one of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9

Number/Computation. addend Any number being added. digit Any one of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 14 Number/Computation addend Any number being added algorithm A step-by-step method for computing array A picture that shows a number of items arranged in rows and columns to form a rectangle associative

More information

Possible solutions, (depending on further analysis)

Possible solutions, (depending on further analysis) Below is one that has been successful in helping people "sharpen their eyes" in looking for risk factors. Possible solutions to each problem are also listed. And (surprise!) there are almost always SEVERAL

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

Nicholas J. Giordano. Chapter 24. Geometrical Optics. Marilyn Akins, PhD Broome Community College

Nicholas J. Giordano.   Chapter 24. Geometrical Optics. Marilyn Akins, PhD Broome Community College Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 24 Geometrical Optics Marilyn Akins, PhD Broome Community College Optics The study of light is called optics Some highlights in the history

More information

Archdiocese of New York Practice Items

Archdiocese of New York Practice Items Archdiocese of New York Practice Items Mathematics Grade 6 Teacher Sample Packet Unit 5 NY MATH_TE_G6_U5.indd 1 NY MATH_TE_G6_U5.indd 2 1. Horatio s patio is shaped like an isosceles trapezoid. He wants

More information

Photography tripod Why do I Need a Tripod? http://www.bhphotovideo.com/explora/video/buying-guides/what-look-when-you-are-looking-videotripod Tripod Tricks? http://vimeo.com/videoschool/lesson/110/tripod-tricks

More information

Geometry. Instructional Activities:

Geometry. Instructional Activities: GEOMETRY Instructional Activities: Geometry Assessment: A. Direct Instruction A. Quizzes B. Cooperative Learning B. Skill Reviews C. Technology Integration C. Test Prep Questions D. Study Guides D. Chapter

More information

Creating Mercator s Map Projection

Creating Mercator s Map Projection Creating Mercator s Map Projection Andrew Geldean December 17, 2014 Abstract: This map developed by Gerardus Mercator in 1569 is created by producing a cylinder around the globe projecting the surface

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

Shapes & Transformations and Angles & Measurements Spatial Visualization and Reflections a.) b.) c.) d.) a.) b.) c.)

Shapes & Transformations and Angles & Measurements Spatial Visualization and Reflections a.) b.) c.) d.) a.) b.) c.) Chapters 1 & 2 Team Number Name Shapes & Transformations and Angles & Measurements 1.2.1 Spatial Visualization and Reflections 1-47. d.) 1-48. 1-49. 1-50. 1-51. d.) 1-52. On the axes at right, graph the

More information

Covering & Surrounding

Covering & Surrounding Covering & Surrounding Two-Dimensional Measurement and Three-Dimensional Measurement Name: Hour: Table of Contents Investigation 1 Investigation 1.1 page 3 Investigation 1.2 page 7 Investigation 1.3 page

More information

Depth. Common Classification Tasks. Example: AlexNet. Another Example: Inception. Another Example: Inception. Depth

Depth. Common Classification Tasks. Example: AlexNet. Another Example: Inception. Another Example: Inception. Depth Common Classification Tasks Recognition of individual objects/faces Analyze object-specific features (e.g., key points) Train with images from different viewing angles Recognition of object classes Analyze

More information

Exceptional quality digital x-ray. At every speed. At every price.

Exceptional quality digital x-ray. At every speed. At every price. Exceptional quality digital x-ray. At every speed. At every price. Choose your speed. Choose your workstation. Choose the digital x-ray that s chosen by hospitals all over the world. Fujifilm has the digital

More information

Ray Optics. Physics 11. Sources of Light Rays: Self-Luminous Objects. The Ray Model of Light

Ray Optics. Physics 11. Sources of Light Rays: Self-Luminous Objects. The Ray Model of Light Physics 11 Ray Optics Ray Model of Light Reflection Plane Mirrors Spherical Mirrors Ray Tracing Images from a Concave Mirror Images from a Convex Mirror Slide 18-3 The Ray Model of Light Sources of Light

More information

AUTOMATED 4 AXIS ADAYfIVE SCANNING WITH THE DIGIBOTICS LASER DIGITIZER

AUTOMATED 4 AXIS ADAYfIVE SCANNING WITH THE DIGIBOTICS LASER DIGITIZER AUTOMATED 4 AXIS ADAYfIVE SCANNING WITH THE DIGIBOTICS LASER DIGITIZER INTRODUCTION The DIGIBOT 3D Laser Digitizer is a high performance 3D input device which combines laser ranging technology, personal

More information

Exceptional quality digital x-ray. At every speed. At every price.

Exceptional quality digital x-ray. At every speed. At every price. Exceptional quality digital x-ray. At every speed. At every price. Choose your speed. Choose your workstation. Choose the digital x-ray that s chosen by hospitals all over the world. Fujifilm has the digital

More information

TV & Office Solutions by equip solutions with a high value of benefit

TV & Office Solutions by equip solutions with a high value of benefit TV & Office Solutions by equip solutions with a high value of benefit The brand equip stands for a product development driven by quality management and continuous adjustments to the requirements of the

More information

Activity 1 Look at the pattern on the number line and find the missing numbers. Model. (b) (c) (a) (b) (c) (d)

Activity 1 Look at the pattern on the number line and find the missing numbers. Model. (b) (c) (a) (b) (c) (d) Lesson Look at the pattern on the number line and find the missing numbers. Model (a) (b) (c) 9 Answers: (a) (b) (c) (a) (b) (c) (a) (b) (c) (a) (b) (c) 00 00. (a) (b) 00. (c) 0 0 (a) (b) (c) Use the number

More information

3D Rendering and Ray Casting

3D Rendering and Ray Casting 3D Rendering and Ray Casting Michael Kazhdan (601.457/657) HB Ch. 13.7, 14.6 FvDFH 15.5, 15.10 Rendering Generate an image from geometric primitives Rendering Geometric Primitives (3D) Raster Image (2D)

More information

PHY 171 Lecture 6 (January 18, 2012)

PHY 171 Lecture 6 (January 18, 2012) PHY 171 Lecture 6 (January 18, 2012) Light Throughout most of the next 2 weeks, we will be concerned with the wave properties of light, and phenomena based on them (interference & diffraction). Light also

More information

Summer Math Packet for Rising 8 th Grade Students

Summer Math Packet for Rising 8 th Grade Students Name This assignment provides a review of mathematical and algebraic skills that are required for success in 8 th grade accelerated math class. Students, please use the packets as a review to help you

More information

Section 12.1 Translations and Rotations

Section 12.1 Translations and Rotations Section 12.1 Translations and Rotations Any rigid motion that preserves length or distance is an isometry. We look at two types of isometries in this section: translations and rotations. Translations A

More information

Boardworks Ltd KS3 Mathematics. S1 Lines and Angles

Boardworks Ltd KS3 Mathematics. S1 Lines and Angles 1 KS3 Mathematics S1 Lines and Angles 2 Contents S1 Lines and angles S1.1 Labelling lines and angles S1.2 Parallel and perpendicular lines S1.3 Calculating angles S1.4 Angles in polygons 3 Lines In Mathematics,

More information

Grade 9 Math Terminology

Grade 9 Math Terminology Unit 1 Basic Skills Review BEDMAS a way of remembering order of operations: Brackets, Exponents, Division, Multiplication, Addition, Subtraction Collect like terms gather all like terms and simplify as

More information

Number Sense and Operations Curriculum Framework Learning Standard

Number Sense and Operations Curriculum Framework Learning Standard Grade 5 Expectations in Mathematics Learning Standards from the MA Mathematics Curriculum Framework for the end of Grade 6 are numbered and printed in bold. The Franklin Public School System s grade level

More information

Geometry Sem 2 REVIEW for Final Part A ink spring notebook. April 19, m. 7' 25' x. 18 m

Geometry Sem 2 REVIEW for Final Part A ink spring notebook. April 19, m. 7' 25' x. 18 m Geometry Sem 2 Review for Final Find the missing sides of each triangle. Leave answers as simplified radicals. 1. m 2. Part 4' 60 n 30 15 m 60 y m =, n = =, y = Find the missing sides of each triangle.

More information

Vocabulary (Return to Links) Circle, square, rectangle, triangle, diamond, trapezoid, parallelogram, rhombus

Vocabulary (Return to Links) Circle, square, rectangle, triangle, diamond, trapezoid, parallelogram, rhombus Viisuall & Perfformiing Artts Program,, SJUSD Artts & Matth Connecttiions Title/Description of Lesson Geometric Shapes through Movement Grade Level: : 2-4 (Possibly 5) Lesson Links Objectives/Outcomes

More information

Ganado Unified School District 7 th Grade Mathematics

Ganado Unified School District 7 th Grade Mathematics Ganado Unified School District 7 th Grade Mathematics PACING Guide SY 2014-2015 Quarter 3 Week 1 Graphs Text Reference Concept : Use random sampling to draw inferences about population. 7.SP.A.1. Understand

More information

6. If QRSTU is a regular pentagon, what is the measure of T? 1. If STUV is a parallelogram, what are the coordinates of point U?

6. If QRSTU is a regular pentagon, what is the measure of T? 1. If STUV is a parallelogram, what are the coordinates of point U? 1. If UV is a parallelogram, what are the coordinates of point U?. If RU is a regular pentagon, what is the measure of? (0, y) U(?,?) (, 0) V( + z, 0) 7. hree siblings are to share an inheritance of $1,0

More information

Pre-Algebra Notes Unit 10: Geometric Figures & Their Properties; Volume

Pre-Algebra Notes Unit 10: Geometric Figures & Their Properties; Volume Pre-Algebra Notes Unit 0: Geometric Figures & Their Properties; Volume Triangles, Quadrilaterals, and Polygons Syllabus Objectives: (4.6) The student will validate conclusions about geometric figures and

More information

Kinematics and Orientations

Kinematics and Orientations Kinematics and Orientations Hierarchies Forward Kinematics Transformations (review) Euler angles Quaternions Yaw and evaluation function for assignment 2 Building a character Just translate, rotate, and

More information

Geo, Chap 8 Practice Test, EV Ver 1

Geo, Chap 8 Practice Test, EV Ver 1 Name: Class: Date: ID: A Geo, Chap 8 Practice Test, EV Ver 1 Short Answer Find the length of the missing side. Leave your answer in simplest radical form. 1. (8-1) 2. (8-1) A grid shows the positions of

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

Geometry Vocabulary. acute angle-an angle measuring less than 90 degrees

Geometry Vocabulary. acute angle-an angle measuring less than 90 degrees Geometry Vocabulary acute angle-an angle measuring less than 90 degrees angle-the turn or bend between two intersecting lines, line segments, rays, or planes angle bisector-an angle bisector is a ray that

More information

Page 1. Right Triangles The Pythagorean Theorem Independent Practice

Page 1. Right Triangles The Pythagorean Theorem Independent Practice Name Date Page 1 Right Triangles The Pythagorean Theorem Independent Practice 1. Tony wants his white picket fence row to have ivy grow in a certain direction. He decides to run a metal wire diagonally

More information

6 Mathematics Curriculum

6 Mathematics Curriculum New York State Common Core 6 Mathematics Curriculum GRADE GRADE 6 MODULE 5 Table of Contents 1 Area, Surface Area, and Volume Problems... 3 Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)...

More information

MATHEMATICS Geometry Standard: Number, Number Sense and Operations

MATHEMATICS Geometry Standard: Number, Number Sense and Operations Standard: Number, Number Sense and Operations Number and Number A. Connect physical, verbal and symbolic representations of 1. Connect physical, verbal and symbolic representations of Systems integers,

More information

Another option is a clamping device that has a camera screw adapter attached to it.

Another option is a clamping device that has a camera screw adapter attached to it. Tripods and Camera Supports When beginners first start using their cameras seriously, they may tend to think of a tripod or other camera support only being necessary when the shutter speed gets to slow

More information

GEOMETRY REVIEW PACKET

GEOMETRY REVIEW PACKET Obstacles are those frightful things you see when you take your eyes off your goal -Henry Ford As of Spring 2016, geometry is no longer a prerequisite for MTH101 and MTH165 Spend time with the material

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

WEEKS 1-2 MECHANISMS

WEEKS 1-2 MECHANISMS References WEEKS 1-2 MECHANISMS (METU, Department of Mechanical Engineering) Text Book: Mechanisms Web Page: http://www.me.metu.edu.tr/people/eres/me301/in dex.ht Analitik Çözümlü Örneklerle Mekanizma

More information

Name Date Class. When the bases are the same and you multiply, you add exponents. When the bases are the same and you divide, you subtract exponents.

Name Date Class. When the bases are the same and you multiply, you add exponents. When the bases are the same and you divide, you subtract exponents. 2-1 Integer Exponents A positive exponent tells you how many times to multiply the base as a factor. A negative exponent tells you how many times to divide by the base. Any number to the 0 power is equal

More information

Digital 3D technologies

Digital 3D technologies Digital 3D technologies A simple introduction Marco Callieri ISTI-CNR callieri@isti.cnr.it Who Am I? Marco Callieri Master Degree & PhD in computer science Researcher at the Visual Computing Lab, ISTI-CNR,

More information

Introduction to 3D Concepts

Introduction to 3D Concepts PART I Introduction to 3D Concepts Chapter 1 Scene... 3 Chapter 2 Rendering: OpenGL (OGL) and Adobe Ray Tracer (ART)...19 1 CHAPTER 1 Scene s0010 1.1. The 3D Scene p0010 A typical 3D scene has several

More information

Grades 7 & 8, Math Circles 20/21/22 February, D Geometry

Grades 7 & 8, Math Circles 20/21/22 February, D Geometry Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing 2D Geometry Review Grades 7 & 8, Math Circles 20/21/22 February, 2018 3D Geometry Two-dimensional shapes

More information

11.1 Rigid Motions. Symmetry

11.1 Rigid Motions. Symmetry 11.1 Rigid Motions Rigid Motions We will now take a closer look at the ideas behind the different types of symmetries that we have discussed by studying four different rigid motions. The act of taking

More information

CGS 3220 Lecture 13 Polygonal Character Modeling

CGS 3220 Lecture 13 Polygonal Character Modeling CGS 3220 Lecture 13 Polygonal Character Modeling Introduction to Computer Aided Modeling Instructor: Brent Rossen Overview Box modeling Polygon proxy Mirroring Polygonal components Topology editing Procedural

More information

BONE CONTROLLER ASSET VERSION 0.1 REV 1

BONE CONTROLLER ASSET VERSION 0.1 REV 1 Foreword Thank you for purchasing the Bone Controller! I m an independent developer and your feedback and support really means a lot to me. Please don t ever hesitate to contact me if you have a question,

More information

Computational Geometry. Definition, Application Areas, and Course Overview

Computational Geometry. Definition, Application Areas, and Course Overview Computational Geometry Definition, Application Areas, and Course Overview Computational Geometry is a subfield of the Design and Analysis of Algorithms Computational Geometry is a subfield of the Design

More information

Assembly Instructions

Assembly Instructions Assembly Instructions Flat Screen Garage End User & IT Computer Cable Management May 2013 nylon zip-tie #2 (for computer wires) rear-access beam door (open) Figure 1 nylon zip-tie #1 (for #1 motor control

More information

Getting Ready to Teach Unit 6

Getting Ready to Teach Unit 6 Getting Ready to Teach Unit 6 Learning Path in the Common Core Standards In this unit, students study the attributes of triangles, quadrilaterals, and other polygons. They find perimeter and area of various

More information

Brunswick School Department: Grade 5

Brunswick School Department: Grade 5 Understandings Questions Mathematics Lines are the fundamental building blocks of polygons. Different tools are used to measure different things. Standard units provide common language for communicating

More information

3D Rendering and Ray Casting

3D Rendering and Ray Casting 3D Rendering and Ray Casting Michael Kazhdan (601.457/657) HB Ch. 13.7, 14.6 FvDFH 15.5, 15.10 Rendering Generate an image from geometric primitives Rendering Geometric Primitives (3D) Raster Image (2D)

More information

Final Project. Houdini

Final Project. Houdini Final Project Houdini Houdini (Apprentice Edition) Download from https://www.sidefx.com/download/ install run etc need to create account Loading OBJ Loading OBJ hover mouse and hit tab Loading OBJ Loading

More information

Universiteit Leiden Computer Science

Universiteit Leiden Computer Science Universiteit Leiden Computer Science Optimizing octree updates for visibility determination on dynamic scenes Name: Hans Wortel Student-no: 0607940 Date: 28/07/2011 1st supervisor: Dr. Michael Lew 2nd

More information

6-3 Rotations. The coordinates are R (7, 8), S (7, 2), and T. esolutions Manual - Powered by Cognero Page 1

6-3 Rotations. The coordinates are R (7, 8), S (7, 2), and T. esolutions Manual - Powered by Cognero Page 1 1. Triangle RST represents the placement of Tyra's tricycle in the driveway and has vertices R( 7, 8), S( 7, 2), and T( 2, 2). Graph the figure and its rotated image after a clockwise rotation of 180 about

More information

So we have been talking about 3D viewing, the transformations pertaining to 3D viewing. Today we will continue on it. (Refer Slide Time: 1:15)

So we have been talking about 3D viewing, the transformations pertaining to 3D viewing. Today we will continue on it. (Refer Slide Time: 1:15) Introduction to Computer Graphics Dr. Prem Kalra Department of Computer Science and Engineering Indian Institute of Technology, Delhi Lecture - 8 3D Viewing So we have been talking about 3D viewing, the

More information

TopMill TopTurn. Jobshop Programming & Simulation for Multi-Side & Complete Mill-Turn Machining for every CNC Control

TopMill TopTurn. Jobshop Programming & Simulation for Multi-Side & Complete Mill-Turn Machining for every CNC Control MEKAMS MillTurnSim TopCAM TopCAT Jobshop Programming & Simulation for Multi-Side & Complete Mill-Turn Machining for every CNC Control 2 Jobshop Programming for Multi-Side and Complete Mill-Turn Machining

More information

GLIDECAM CAMCRANE 200TM. Set-up and Operations Guide

GLIDECAM CAMCRANE 200TM. Set-up and Operations Guide GLIDECAM CAMCRANE 200TM Set-up and Operations Guide Glidecam Industries, Inc. 23 Joseph Street, Kingston, MA 02364 Customer Service Line (781) 585-7900 Manufactured in the U.S.A. COPYRIGHT 2000-2008 GLIDECAM

More information

Broadcast & Studio fluid Heads

Broadcast & Studio fluid Heads Broadcast & Studio fluid Heads Compact versatile the MASTER MK2 counterbalances very light cameras from 3 Kg (. lbs) all the way to 3 Kg ( lbs) making the Mk2 suitable from the smallest camera to fully

More information

12 m. 30 m. The Volume of a sphere is 36 cubic units. Find the length of the radius.

12 m. 30 m. The Volume of a sphere is 36 cubic units. Find the length of the radius. NAME DATE PER. REVIEW #18: SPHERES, COMPOSITE FIGURES, & CHANGING DIMENSIONS PART 1: SURFACE AREA & VOLUME OF SPHERES Find the measure(s) indicated. Answers to even numbered problems should be rounded

More information

5 Applications of Definite Integrals

5 Applications of Definite Integrals 5 Applications of Definite Integrals The previous chapter introduced the concepts of a definite integral as an area and as a limit of Riemann sums, demonstrated some of the properties of integrals, introduced

More information

Improving Vision-Based Distance Measurements using Reference Objects

Improving Vision-Based Distance Measurements using Reference Objects Improving Vision-Based Distance Measurements using Reference Objects Matthias Jüngel, Heinrich Mellmann, and Michael Spranger Humboldt-Universität zu Berlin, Künstliche Intelligenz Unter den Linden 6,

More information

CV: 3D to 2D mathematics. Perspective transformation; camera calibration; stereo computation; and more

CV: 3D to 2D mathematics. Perspective transformation; camera calibration; stereo computation; and more CV: 3D to 2D mathematics Perspective transformation; camera calibration; stereo computation; and more Roadmap of topics n Review perspective transformation n Camera calibration n Stereo methods n Structured

More information

CCM6+ Unit 12 Surface Area and Volume page 1 CCM6+ UNIT 12 Surface Area and Volume Name Teacher Kim Li

CCM6+ Unit 12 Surface Area and Volume page 1 CCM6+ UNIT 12 Surface Area and Volume Name Teacher Kim Li CCM6+ Unit 12 Surface Area and Volume page 1 CCM6+ UNIT 12 Surface Area and Volume Name Teacher Kim Li MAIN CONCEPTS Page(s) Unit 12 Vocabulary 2 3D Figures 3-8 Volume of Prisms 9-19 Surface Area 20-26

More information

Number of sides Name of polygon Least number of Interior angle sum 3 Triangle

Number of sides Name of polygon Least number of Interior angle sum 3 Triangle Name: Period: 6.1 Polygon Sum Polygon: a closed plane figure formed by three or more segments that intersect only at their endpoints. Are these polygons? If so, classify it by the number of sides. 1) 2)

More information

2. The vertices of Δ ABC are A( 1, 2), B( 1,2), and C(6,0). Which conclusion can be made about the angles of Δ ABC?

2. The vertices of Δ ABC are A( 1, 2), B( 1,2), and C(6,0). Which conclusion can be made about the angles of Δ ABC? 1 Line k is drawn so that it is perpendicular to two distinct planes, P and R. What must be true about planes P and R? A. Planes P and R are skew B. Planes P and R are perpendicular. C. Planes P and R

More information

LECTURE 7. Announcements

LECTURE 7. Announcements LECTURE 7 Announcements Minecraft 4 Feedback Looks good! A game that minimally involves platforms Not based on any game in particular Super Mario 64? Team Fortress 2? Completely up to you to make unique

More information