1 Drawing 3D Objects in Adobe Illustrator

Size: px
Start display at page:

Download "1 Drawing 3D Objects in Adobe Illustrator"

Transcription

1 Drwing 3D Objects in Adobe Illustrtor 1 1 Drwing 3D Objects in Adobe Illustrtor This Tutoril will show you how to drw simple objects with three-dimensionl ppernce. At first we will drw rrows indicting movement in 3D spce. Adobe Illustrtor 7.0 ws used to crete the following grphics, but ll procedures re vlid for newer versions (up to CS2), too. In the first section you ll find some bsic informtion bout isometric views ( specil kind of drwing, which is lmost stndrd for technicl illustrtion) The second section describes the steps necessry to crete the corresponding drwings using Adobe Illustrtor. And now... hve fun nd crete gret grphics :-) Bernd Meissner e-mil: info@meissner-dokutem.de P.S.: English is not my ntive lnguge, so ny corrections re welcome Bernd Meissner 1

2 1 Drwing 3D Objects in Adobe Illustrtor 1.1 Bsics of Isometric Projection +90 Z Y 90 X Bernd Meissner

3 Drwing 3D Objects in Adobe Illustrtor 1 Isometric projections re two-dimensionl drwing of three-dimensionl objects, creted by prllel projection. Objects look like hving volume, without ctully hving one. The min chrcteristics of n isometric projection re: there is no vnishing point lines tht re prllel in relity will be prllel in the drwing sme lenghts in relity will be drwn t the sme length, without ny shortening cused by perspective view. An isometric drwing is creted long the xes representing the 3D spce: Red xes mrk the 2D spce (like sheet of pper), s found in typicl drwing pplictions (e.g. Adobe Illustrtor, FreeHnd). You ll find n xis nmed x nd n xis nmed y, drwn t their respective ngles. Blue xes mrk the three dimensions (x, y, z) of 3D spce. The ngle between x/z, y/z nd y/x is equivlent to 90 (in 3D spce) nd is drwn t 120 in 2D spce (red) Bernd Meissner 3

4 1 Drwing 3D Objects in Adobe Illustrtor Prcticlly this results in two simple rules for drwing: Dimension (x, y) of the qudrtic shpe (red) cn be directly used on the isometric xes x, y (blue) When the bsic shpe of the object (here: cube) is drwn, the correspondig fces cn simply be creted by double 120 rottion of the shpe Bernd Meissner

5 Drwing 3D Objects in Adobe Illustrtor Isometric Projections using Illustrtor Isometric objects cn be creted out of 2D shpes using the Distortion Tool. Since this tool produces nonproportionl distortions (resulting edges hve different lengths), this error must be corrected by pplying known scling fctor before distorting the shpe. Flt Arrows The following instructions pply to flt objects, tht will be positioned on one of the three plnes (x/y, y/z, y/x). Crete the bsic shpe in top view Select the object nd open the Scle Tool options. Enter non-proportionl scling using fctor of 86,602% horizontlly nd 100% verticlly Bernd Meissner 5

6 1 Drwing 3D Objects in Adobe Illustrtor Now select the Distortion Tool. Enter distortion ngle of 30 long the verticl xis. This setting mens, tht verticl lines re just moved verticlly, while horizontl lines re tilt by 30. Without the preceding scling, the horizontl lines would get longer thn the verticl lines t this moment. Finlly you hve creted n rrow, which is correctly displyed s n isometric object, positioned in the x/z plne. This rrow fits to ny other object, which is drwn s n isometric body Bernd Meissner

7 Drwing 3D Objects in Adobe Illustrtor 1 The esiest wy to crete n rrow within the y/z plne is mirroring copy long the verticl xis. If you rotte copies of these two rrows round 120, you ll get whole librry of isometric rrows t vrious positions nd directions. Missing rrows cn now be creted by further mirroring long the horizontl xis Bernd Meissner 7

8 1 Drwing 3D Objects in Adobe Illustrtor 3D Arrows Using the rrows s creted before you cn simply build rrows moving through 3D spce. The following exmple demonstrtes the rottion of cylindricl object. Drw circle with rdius, tht s significntly lrger thn the cylindricl object s rdius. Plce the center of the circle onto the center of the upper cylinder fce. Now crete n isometric ellipse from the circle s described before (scle, distort, rotte). Copy n rrow (upright stnding) from your newly creted librry nd shorten its shft by moving the endpoints upwrds. Now rotte/mirror the resulting rrowhed s shown on the left Bernd Meissner

9 Drwing 3D Objects in Adobe Illustrtor 1 Plce the rrowhed onto the ellipse (shown in red). Try to mtch the directions of rrow nd ellipse by choosing the pproprite position on the ellipse. Cut the ellipse s desired nd delete the unecessry prts. Now plce the corner point of the rrowhed exctly onto the ellipse s end point (blue). Cut the remining prt of the ellipse gin t the outmost (here: rightmost) point of the curve Bernd Meissner 9

10 1 Drwing 3D Objects in Adobe Illustrtor Select both segments (shown in different colors for better distinction) nd move copy to the lower corner point of the rrowhed, s shown on the left. Select both end points of the blue segments nd Join them using the corresponding commnd. Close the other end of the new object s well. Assign ny fill color to the new object. Now cut the rrow t the mrked points nd delete the segment between them (the rrow is no longer closed shpe). Join the end points of the rrow nd the corresponding end points of the (red) ellipse prts. Assign contour nd fill color to the front prt of the rrow. If necessry, move the prts of the rrow to the front or bck Bernd Meissner

11 Drwing 3D Objects in Adobe Illustrtor 1 As lredy done before, you my mirror (horizontlly) nd rotte (2 x 120 ) the rrow in order to use it on different xes of the isometric 3d spce Bernd Meissner 11

12 1 Drwing 3D Objects in Adobe Illustrtor Bernd Meissner

Geometric transformations

Geometric transformations Geometric trnsformtions Computer Grphics Some slides re bsed on Shy Shlom slides from TAU mn n n m m T A,,,,,, 2 1 2 22 12 1 21 11 Rows become columns nd columns become rows nm n n m m A,,,,,, 1 1 2 22

More information

Section 10.4 Hyperbolas

Section 10.4 Hyperbolas 66 Section 10.4 Hyperbols Objective : Definition of hyperbol & hyperbols centered t (0, 0). The third type of conic we will study is the hyperbol. It is defined in the sme mnner tht we defined the prbol

More information

Class-XI Mathematics Conic Sections Chapter-11 Chapter Notes Key Concepts

Class-XI Mathematics Conic Sections Chapter-11 Chapter Notes Key Concepts Clss-XI Mthemtics Conic Sections Chpter-11 Chpter Notes Key Concepts 1. Let be fixed verticl line nd m be nother line intersecting it t fixed point V nd inclined to it t nd ngle On rotting the line m round

More information

Stained Glass Design. Teaching Goals:

Stained Glass Design. Teaching Goals: Stined Glss Design Time required 45-90 minutes Teching Gols: 1. Students pply grphic methods to design vrious shpes on the plne.. Students pply geometric trnsformtions of grphs of functions in order to

More information

MATH 2530: WORKSHEET 7. x 2 y dz dy dx =

MATH 2530: WORKSHEET 7. x 2 y dz dy dx = MATH 253: WORKSHT 7 () Wrm-up: () Review: polr coordintes, integrls involving polr coordintes, triple Riemnn sums, triple integrls, the pplictions of triple integrls (especilly to volume), nd cylindricl

More information

6.2 Volumes of Revolution: The Disk Method

6.2 Volumes of Revolution: The Disk Method mth ppliction: volumes by disks: volume prt ii 6 6 Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem 6) nd the ccumultion process is to determine so-clled volumes

More information

Naming 3D objects. 1 Name the 3D objects labelled in these models. Use the word bank to help you.

Naming 3D objects. 1 Name the 3D objects labelled in these models. Use the word bank to help you. Nming 3D ojects 1 Nme the 3D ojects lelled in these models. Use the word nk to help you. Word nk cue prism sphere cone cylinder pyrmid D A C F A B C D cone cylinder cue cylinder E B E prism F cue G G pyrmid

More information

Grade 7/8 Math Circles Geometric Arithmetic October 31, 2012

Grade 7/8 Math Circles Geometric Arithmetic October 31, 2012 Fculty of Mthemtics Wterloo, Ontrio N2L 3G1 Grde 7/8 Mth Circles Geometric Arithmetic Octoer 31, 2012 Centre for Eduction in Mthemtics nd Computing Ancient Greece hs given irth to some of the most importnt

More information

9.1 apply the distance and midpoint formulas

9.1 apply the distance and midpoint formulas 9.1 pply the distnce nd midpoint formuls DISTANCE FORMULA MIDPOINT FORMULA To find the midpoint between two points x, y nd x y 1 1,, we Exmple 1: Find the distnce between the two points. Then, find the

More information

10.5 Graphing Quadratic Functions

10.5 Graphing Quadratic Functions 0.5 Grphing Qudrtic Functions Now tht we cn solve qudrtic equtions, we wnt to lern how to grph the function ssocited with the qudrtic eqution. We cll this the qudrtic function. Grphs of Qudrtic Functions

More information

Pythagoras theorem and trigonometry (2)

Pythagoras theorem and trigonometry (2) HPTR 10 Pythgors theorem nd trigonometry (2) 31 HPTR Liner equtions In hpter 19, Pythgors theorem nd trigonometry were used to find the lengths of sides nd the sizes of ngles in right-ngled tringles. These

More information

1 Quad-Edge Construction Operators

1 Quad-Edge Construction Operators CS48: Computer Grphics Hndout # Geometric Modeling Originl Hndout #5 Stnford University Tuesdy, 8 December 99 Originl Lecture #5: 9 November 99 Topics: Mnipultions with Qud-Edge Dt Structures Scribe: Mike

More information

6.3 Volumes. Just as area is always positive, so is volume and our attitudes towards finding it.

6.3 Volumes. Just as area is always positive, so is volume and our attitudes towards finding it. 6.3 Volumes Just s re is lwys positive, so is volume nd our ttitudes towrds finding it. Let s review how to find the volume of regulr geometric prism, tht is, 3-dimensionl oject with two regulr fces seprted

More information

5 Regular 4-Sided Composition

5 Regular 4-Sided Composition Xilinx-Lv User Guide 5 Regulr 4-Sided Composition This tutoril shows how regulr circuits with 4-sided elements cn be described in Lv. The type of regulr circuits tht re discussed in this tutoril re those

More information

If f(x, y) is a surface that lies above r(t), we can think about the area between the surface and the curve.

If f(x, y) is a surface that lies above r(t), we can think about the area between the surface and the curve. Line Integrls The ide of line integrl is very similr to tht of single integrls. If the function f(x) is bove the x-xis on the intervl [, b], then the integrl of f(x) over [, b] is the re under f over the

More information

Fall 2018 Midterm 1 October 11, ˆ You may not ask questions about the exam except for language clarifications.

Fall 2018 Midterm 1 October 11, ˆ You may not ask questions about the exam except for language clarifications. 15-112 Fll 2018 Midterm 1 October 11, 2018 Nme: Andrew ID: Recittion Section: ˆ You my not use ny books, notes, extr pper, or electronic devices during this exm. There should be nothing on your desk or

More information

Tilt-Sensing with Kionix MEMS Accelerometers

Tilt-Sensing with Kionix MEMS Accelerometers Tilt-Sensing with Kionix MEMS Accelerometers Introduction Tilt/Inclintion sensing is common ppliction for low-g ccelerometers. This ppliction note describes how to use Kionix MEMS low-g ccelerometers to

More information

Graphing Conic Sections

Graphing Conic Sections Grphing Conic Sections Definition of Circle Set of ll points in plne tht re n equl distnce, clled the rdius, from fixed point in tht plne, clled the center. Grphing Circle (x h) 2 + (y k) 2 = r 2 where

More information

B. Definition: The volume of a solid of known integrable cross-section area A(x) from x = a

B. Definition: The volume of a solid of known integrable cross-section area A(x) from x = a Mth 176 Clculus Sec. 6.: Volume I. Volume By Slicing A. Introduction We will e trying to find the volume of solid shped using the sum of cross section res times width. We will e driving towrd developing

More information

Chapter44. Polygons and solids. Contents: A Polygons B Triangles C Quadrilaterals D Solids E Constructing solids

Chapter44. Polygons and solids. Contents: A Polygons B Triangles C Quadrilaterals D Solids E Constructing solids Chpter44 Polygons nd solids Contents: A Polygons B Tringles C Qudrilterls D Solids E Constructing solids 74 POLYGONS AND SOLIDS (Chpter 4) Opening prolem Things to think out: c Wht different shpes cn you

More information

Ray surface intersections

Ray surface intersections Ry surfce intersections Some primitives Finite primitives: polygons spheres, cylinders, cones prts of generl qudrics Infinite primitives: plnes infinite cylinders nd cones generl qudrics A finite primitive

More information

3 4. Answers may vary. Sample: Reteaching Vertical s are.

3 4. Answers may vary. Sample: Reteaching Vertical s are. Chpter 7 Answers Alterntive Activities 7-2 1 2. Check students work. 3. The imge hs length tht is 2 3 tht of the originl segment nd is prllel to the originl segment. 4. The segments pss through the endpoints

More information

UNIVERSITY OF EDINBURGH COLLEGE OF SCIENCE AND ENGINEERING SCHOOL OF INFORMATICS INFORMATICS 1 COMPUTATION & LOGIC INSTRUCTIONS TO CANDIDATES

UNIVERSITY OF EDINBURGH COLLEGE OF SCIENCE AND ENGINEERING SCHOOL OF INFORMATICS INFORMATICS 1 COMPUTATION & LOGIC INSTRUCTIONS TO CANDIDATES UNIVERSITY OF EDINBURGH COLLEGE OF SCIENCE AND ENGINEERING SCHOOL OF INFORMATICS INFORMATICS COMPUTATION & LOGIC Sturdy st April 7 : to : INSTRUCTIONS TO CANDIDATES This is tke-home exercise. It will not

More information

Lecture 7: Building 3D Models (Part 1) Prof Emmanuel Agu. Computer Science Dept. Worcester Polytechnic Institute (WPI)

Lecture 7: Building 3D Models (Part 1) Prof Emmanuel Agu. Computer Science Dept. Worcester Polytechnic Institute (WPI) Computer Grphics (CS 4731) Lecture 7: Building 3D Models (Prt 1) Prof Emmnuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI) Stndrd d Unit itvectors Define y i j 1,0,0 0,1,0 k i k 0,0,1

More information

Hyperbolas. Definition of Hyperbola

Hyperbolas. Definition of Hyperbola CHAT Pre-Clculus Hyperols The third type of conic is clled hyperol. For n ellipse, the sum of the distnces from the foci nd point on the ellipse is fixed numer. For hyperol, the difference of the distnces

More information

PNC NC code PROGRAMMER'S MANUAL

PNC NC code PROGRAMMER'S MANUAL PNC-3200 NC code PROGRAMMER'S MANUAL Thnk you very much for purchsing the PNC-3200. To ensure correct nd sfe usge with full understnding of this product's performnce, plese be sure to red through this

More information

Conic Sections Parabola Objective: Define conic section, parabola, draw a parabola, standard equations and their graphs

Conic Sections Parabola Objective: Define conic section, parabola, draw a parabola, standard equations and their graphs Conic Sections Prol Ojective: Define conic section, prol, drw prol, stndrd equtions nd their grphs The curves creted y intersecting doule npped right circulr cone with plne re clled conic sections. If

More information

INTRODUCTION TO SIMPLICIAL COMPLEXES

INTRODUCTION TO SIMPLICIAL COMPLEXES INTRODUCTION TO SIMPLICIAL COMPLEXES CASEY KELLEHER AND ALESSANDRA PANTANO 0.1. Introduction. In this ctivity set we re going to introduce notion from Algebric Topology clled simplicil homology. The min

More information

MTH 146 Conics Supplement

MTH 146 Conics Supplement 105- Review of Conics MTH 146 Conics Supplement In this section we review conics If ou ne more detils thn re present in the notes, r through section 105 of the ook Definition: A prol is the set of points

More information

Date: 9.1. Conics: Parabolas

Date: 9.1. Conics: Parabolas Dte: 9. Conics: Prols Preclculus H. Notes: Unit 9 Conics Conic Sections: curves tht re formed y the intersection of plne nd doulenpped cone Syllus Ojectives:. The student will grph reltions or functions,

More information

50 AMC LECTURES Lecture 2 Analytic Geometry Distance and Lines. can be calculated by the following formula:

50 AMC LECTURES Lecture 2 Analytic Geometry Distance and Lines. can be calculated by the following formula: 5 AMC LECTURES Lecture Anlytic Geometry Distnce nd Lines BASIC KNOWLEDGE. Distnce formul The distnce (d) between two points P ( x, y) nd P ( x, y) cn be clculted by the following formul: d ( x y () x )

More information

HW Stereotactic Targeting

HW Stereotactic Targeting HW Stereotctic Trgeting We re bout to perform stereotctic rdiosurgery with the Gmm Knife under CT guidnce. We instrument the ptient with bse ring nd for CT scnning we ttch fiducil cge (FC). Above: bse

More information

MA1008. Calculus and Linear Algebra for Engineers. Course Notes for Section B. Stephen Wills. Department of Mathematics. University College Cork

MA1008. Calculus and Linear Algebra for Engineers. Course Notes for Section B. Stephen Wills. Department of Mathematics. University College Cork MA1008 Clculus nd Liner Algebr for Engineers Course Notes for Section B Stephen Wills Deprtment of Mthemtics University College Cork s.wills@ucc.ie http://euclid.ucc.ie/pges/stff/wills/teching/m1008/ma1008.html

More information

Mathematics Background

Mathematics Background For more roust techer experience, plese visit Techer Plce t mthdshord.com/cmp3 Mthemtics Bckground Extending Understnding of Two-Dimensionl Geometry In Grde 6, re nd perimeter were introduced to develop

More information

2 Computing all Intersections of a Set of Segments Line Segment Intersection

2 Computing all Intersections of a Set of Segments Line Segment Intersection 15-451/651: Design & Anlysis of Algorithms Novemer 14, 2016 Lecture #21 Sweep-Line nd Segment Intersection lst chnged: Novemer 8, 2017 1 Preliminries The sweep-line prdigm is very powerful lgorithmic design

More information

Unit 5 Vocabulary. A function is a special relationship where each input has a single output.

Unit 5 Vocabulary. A function is a special relationship where each input has a single output. MODULE 3 Terms Definition Picture/Exmple/Nottion 1 Function Nottion Function nottion is n efficient nd effective wy to write functions of ll types. This nottion llows you to identify the input vlue with

More information

such that the S i cover S, or equivalently S

such that the S i cover S, or equivalently S MATH 55 Triple Integrls Fll 16 1. Definition Given solid in spce, prtition of consists of finite set of solis = { 1,, n } such tht the i cover, or equivlently n i. Furthermore, for ech i, intersects i

More information

Area & Volume. Chapter 6.1 & 6.2 September 25, y = 1! x 2. Back to Area:

Area & Volume. Chapter 6.1 & 6.2 September 25, y = 1! x 2. Back to Area: Bck to Are: Are & Volume Chpter 6. & 6. Septemer 5, 6 We cn clculte the re etween the x-xis nd continuous function f on the intervl [,] using the definite integrl:! f x = lim$ f x * i )%x n i= Where fx

More information

CS380: Computer Graphics Modeling Transformations. Sung-Eui Yoon ( 윤성의 ) Course URL:

CS380: Computer Graphics Modeling Transformations. Sung-Eui Yoon ( 윤성의 ) Course URL: CS38: Computer Grphics Modeling Trnsformtions Sung-Eui Yoon ( 윤성의 ) Course URL: http://sgl.kist.c.kr/~sungeui/cg/ Clss Ojectives (Ch. 3.5) Know the clssic dt processing steps, rendering pipeline, for rendering

More information

Yoplait with Areas and Volumes

Yoplait with Areas and Volumes Yoplit with Ares nd Volumes Yoplit yogurt comes in two differently shped continers. One is truncted cone nd the other is n ellipticl cylinder (see photos below). In this exercise, you will determine the

More information

SOME EXAMPLES OF SUBDIVISION OF SMALL CATEGORIES

SOME EXAMPLES OF SUBDIVISION OF SMALL CATEGORIES SOME EXAMPLES OF SUBDIVISION OF SMALL CATEGORIES MARCELLO DELGADO Abstrct. The purpose of this pper is to build up the bsic conceptul frmework nd underlying motivtions tht will llow us to understnd ctegoricl

More information

File Manager Quick Reference Guide. June Prepared for the Mayo Clinic Enterprise Kahua Deployment

File Manager Quick Reference Guide. June Prepared for the Mayo Clinic Enterprise Kahua Deployment File Mnger Quick Reference Guide June 2018 Prepred for the Myo Clinic Enterprise Khu Deployment NVIGTION IN FILE MNGER To nvigte in File Mnger, users will mke use of the left pne to nvigte nd further pnes

More information

CHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE

CHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE CHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE 3.1 Scheimpflug Configurtion nd Perspective Distortion Scheimpflug criterion were found out to be the best lyout configurtion for Stereoscopic PIV, becuse

More information

Digital Design. Chapter 6: Optimizations and Tradeoffs

Digital Design. Chapter 6: Optimizations and Tradeoffs Digitl Design Chpter 6: Optimiztions nd Trdeoffs Slides to ccompny the tetbook Digitl Design, with RTL Design, VHDL, nd Verilog, 2nd Edition, by Frnk Vhid, John Wiley nd Sons Publishers, 2. http://www.ddvhid.com

More information

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1 Mth 33 Volume Stewrt 5.2 Geometry of integrls. In this section, we will lern how to compute volumes using integrls defined by slice nlysis. First, we recll from Clculus I how to compute res. Given the

More information

Here is an example where angles with a common arm and vertex overlap. Name all the obtuse angles adjacent to

Here is an example where angles with a common arm and vertex overlap. Name all the obtuse angles adjacent to djcent tht do not overlp shre n rm from the sme vertex point re clled djcent ngles. me the djcent cute ngles in this digrm rm is shred y + + me vertex point for + + + is djcent to + djcent simply mens

More information

9 Graph Cutting Procedures

9 Graph Cutting Procedures 9 Grph Cutting Procedures Lst clss we begn looking t how to embed rbitrry metrics into distributions of trees, nd proved the following theorem due to Brtl (1996): Theorem 9.1 (Brtl (1996)) Given metric

More information

CS143 Handout 07 Summer 2011 June 24 th, 2011 Written Set 1: Lexical Analysis

CS143 Handout 07 Summer 2011 June 24 th, 2011 Written Set 1: Lexical Analysis CS143 Hndout 07 Summer 2011 June 24 th, 2011 Written Set 1: Lexicl Anlysis In this first written ssignment, you'll get the chnce to ply round with the vrious constructions tht come up when doing lexicl

More information

Order these angles from smallest to largest by wri ng 1 to 4 under each one. Put a check next to the right angle.

Order these angles from smallest to largest by wri ng 1 to 4 under each one. Put a check next to the right angle. Lines nd ngles Connect ech set of lines to the correct nme: prllel perpendiculr Order these ngles from smllest to lrgest y wri ng to 4 under ech one. Put check next to the right ngle. Complete this tle

More information

pdfapilot Server 2 Manual

pdfapilot Server 2 Manual pdfpilot Server 2 Mnul 2011 by clls softwre gmbh Schönhuser Allee 6/7 D 10119 Berlin Germny info@cllssoftwre.com www.cllssoftwre.com Mnul clls pdfpilot Server 2 Pge 2 clls pdfpilot Server 2 Mnul Lst modified:

More information

Section 9.2 Hyperbolas

Section 9.2 Hyperbolas Section 9. Hperols 597 Section 9. Hperols In the lst section, we lerned tht plnets hve pproimtel ellipticl orits round the sun. When n oject like comet is moving quickl, it is le to escpe the grvittionl

More information

1. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES)

1. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES) Numbers nd Opertions, Algebr, nd Functions 45. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES) In sequence of terms involving eponentil growth, which the testing service lso clls geometric

More information

Math 35 Review Sheet, Spring 2014

Math 35 Review Sheet, Spring 2014 Mth 35 Review heet, pring 2014 For the finl exm, do ny 12 of the 15 questions in 3 hours. They re worth 8 points ech, mking 96, with 4 more points for netness! Put ll your work nd nswers in the provided

More information

Lab 1 - Counter. Create a project. Add files to the project. Compile design files. Run simulation. Debug results

Lab 1 - Counter. Create a project. Add files to the project. Compile design files. Run simulation. Debug results 1 L 1 - Counter A project is collection mechnism for n HDL design under specifiction or test. Projects in ModelSim ese interction nd re useful for orgnizing files nd specifying simultion settings. The

More information

In the last lecture, we discussed how valid tokens may be specified by regular expressions.

In the last lecture, we discussed how valid tokens may be specified by regular expressions. LECTURE 5 Scnning SYNTAX ANALYSIS We know from our previous lectures tht the process of verifying the syntx of the progrm is performed in two stges: Scnning: Identifying nd verifying tokens in progrm.

More information

Agilent Mass Hunter Software

Agilent Mass Hunter Software Agilent Mss Hunter Softwre Quick Strt Guide Use this guide to get strted with the Mss Hunter softwre. Wht is Mss Hunter Softwre? Mss Hunter is n integrl prt of Agilent TOF softwre (version A.02.00). Mss

More information

Angle properties of lines and polygons

Angle properties of lines and polygons chievement Stndrd 91031 pply geometric resoning in solving problems Copy correctly Up to 3% of workbook Copying or scnning from ES workbooks is subject to the NZ Copyright ct which limits copying to 3%

More information

MENSURATION-IV

MENSURATION-IV MENSURATION-IV Theory: A solid is figure bounded by one or more surfce. Hence solid hs length, bredth nd height. The plne surfces tht bind solid re clled its fces. The fundmentl difference between plne

More information

Answer Key Lesson 6: Workshop: Angles and Lines

Answer Key Lesson 6: Workshop: Angles and Lines nswer Key esson 6: tudent Guide ngles nd ines Questions 1 3 (G p. 406) 1. 120 ; 360 2. hey re the sme. 3. 360 Here re four different ptterns tht re used to mke quilts. Work with your group. se your Power

More information

Study Sheet ( )

Study Sheet ( ) Key Terms prol circle Ellipse hyperol directrix focus focl length xis of symmetry vertex Study Sheet (11.1-11.4) Conic Section A conic section is section of cone. The ellipse, prol, nd hyperol, long with

More information

CPSC (T1) 2nd Midterm Exam

CPSC (T1) 2nd Midterm Exam Signture: Fire Alrm Code: CPSC 44 2-2 (T) 2nd Midterm Exm Deprtment of Computer Science University of British Columbi K. Booth & R. Schrein Exm Instructions (Red Crefully). Sign the first pge of the exm

More information

Iterated Integrals. f (x; y) dy dx. p(x) To evaluate a type I integral, we rst evaluate the inner integral Z q(x) f (x; y) dy.

Iterated Integrals. f (x; y) dy dx. p(x) To evaluate a type I integral, we rst evaluate the inner integral Z q(x) f (x; y) dy. Iterted Integrls Type I Integrls In this section, we begin the study of integrls over regions in the plne. To do so, however, requires tht we exmine the importnt ide of iterted integrls, in which inde

More information

USING HOUGH TRANSFORM IN LINE EXTRACTION

USING HOUGH TRANSFORM IN LINE EXTRACTION Stylinidis, Efstrtios USING HOUGH TRANSFORM IN LINE EXTRACTION Efstrtios STYLIANIDIS, Petros PATIAS The Aristotle University of Thessloniki, Deprtment of Cdstre Photogrmmetry nd Crtogrphy Univ. Box 473,

More information

Rational Numbers---Adding Fractions With Like Denominators.

Rational Numbers---Adding Fractions With Like Denominators. Rtionl Numbers---Adding Frctions With Like Denomintors. A. In Words: To dd frctions with like denomintors, dd the numertors nd write the sum over the sme denomintor. B. In Symbols: For frctions c nd b

More information

1.1 Lines AP Calculus

1.1 Lines AP Calculus . Lines AP Clculus. LINES Notecrds from Section.: Rules for Rounding Round or Truncte ll finl nswers to 3 deciml plces. Do NOT round before ou rech our finl nswer. Much of Clculus focuses on the concept

More information

called the vertex. The line through the focus perpendicular to the directrix is called the axis of the parabola.

called the vertex. The line through the focus perpendicular to the directrix is called the axis of the parabola. Review of conic sections Conic sections re grphs of the form REVIEW OF CONIC SECTIONS prols ellipses hperols P(, ) F(, p) O p =_p REVIEW OF CONIC SECTIONS In this section we give geometric definitions

More information

9 4. CISC - Curriculum & Instruction Steering Committee. California County Superintendents Educational Services Association

9 4. CISC - Curriculum & Instruction Steering Committee. California County Superintendents Educational Services Association 9. CISC - Curriculum & Instruction Steering Committee The Winning EQUATION A HIGH QUALITY MATHEMATICS PROFESSIONAL DEVELOPMENT PROGRAM FOR TEACHERS IN GRADES THROUGH ALGEBRA II STRAND: NUMBER SENSE: Rtionl

More information

A dual of the rectangle-segmentation problem for binary matrices

A dual of the rectangle-segmentation problem for binary matrices A dul of the rectngle-segmenttion prolem for inry mtrices Thoms Klinowski Astrct We consider the prolem to decompose inry mtrix into smll numer of inry mtrices whose -entries form rectngle. We show tht

More information

TASK SPECIFIC DESCRIPTION

TASK SPECIFIC DESCRIPTION MYP Algebr II/Trig Unit 2 Ch. 4 Trnsformtions Project Nme: Block: - Due Dte: Tuesdy, 11/7 (B-dy) & Wednesdy, 11/8 (A-dy) Mterils: Grph pper, ruler, protrctor, compss, highlight mrkers/colored pencils SCORE:

More information

12-B FRACTIONS AND DECIMALS

12-B FRACTIONS AND DECIMALS -B Frctions nd Decimls. () If ll four integers were negtive, their product would be positive, nd so could not equl one of them. If ll four integers were positive, their product would be much greter thn

More information

Series LJ1. Uniaxial Electric Actuator

Series LJ1. Uniaxial Electric Actuator CAT.E 90- Unixil Electric Actutor Controller Teching Box Unixil Electric Actutor Series LJ Series LJ Series LC Series LC for horizontl mounting nd brke for verticl mounting hve been dded to the high rigidity

More information

Fall 2018 Midterm 2 November 15, 2018

Fall 2018 Midterm 2 November 15, 2018 Nme: 15-112 Fll 2018 Midterm 2 November 15, 2018 Andrew ID: Recittion Section: ˆ You my not use ny books, notes, extr pper, or electronic devices during this exm. There should be nothing on your desk or

More information

Angle Properties in Polygons. Part 1 Interior Angles

Angle Properties in Polygons. Part 1 Interior Angles 2.4 Angle Properties in Polygons YOU WILL NEED dynmic geometry softwre OR protrctor nd ruler EXPLORE A pentgon hs three right ngles nd four sides of equl length, s shown. Wht is the sum of the mesures

More information

Epson Projector Content Manager Operation Guide

Epson Projector Content Manager Operation Guide Epson Projector Content Mnger Opertion Guide Contents 2 Introduction to the Epson Projector Content Mnger Softwre 3 Epson Projector Content Mnger Fetures... 4 Setting Up the Softwre for the First Time

More information

PicoScope 6. PC Oscilloscope Software. User's Guide. psw.en r46

PicoScope 6. PC Oscilloscope Software. User's Guide. psw.en r46 PicoScope 6 PC Oscilloscope Softwre User's Guide PicoScope 6 User's Guide I Tble of Contents 1 Welcome... 1 2 Introduction... 4 1 Legl sttement... 4 2 Updtes... 4 3 Trde mrks... 4 4 System requirements...

More information

4-1 NAME DATE PERIOD. Study Guide. Parallel Lines and Planes P Q, O Q. Sample answers: A J, A F, and D E

4-1 NAME DATE PERIOD. Study Guide. Parallel Lines and Planes P Q, O Q. Sample answers: A J, A F, and D E 4-1 NAME DATE PERIOD Pges 142 147 Prllel Lines nd Plnes When plnes do not intersect, they re sid to e prllel. Also, when lines in the sme plne do not intersect, they re prllel. But when lines re not in

More information

Welch Allyn CardioPerfect Workstation Installation Guide

Welch Allyn CardioPerfect Workstation Installation Guide Welch Allyn CrdioPerfect Worksttion Instlltion Guide INSTALLING CARDIOPERFECT WORKSTATION SOFTWARE & ACCESSORIES ON A SINGLE PC For softwre version 1.6.6 or lter For network instlltion, plese refer to

More information

Easy Interactive Tools Ver.3.0 Operation Guide

Easy Interactive Tools Ver.3.0 Operation Guide Esy Interctive Tools Ver.3.0 Opertion Guide Esy Interctive Tools Summry 2 Fetures Esy Interctive Tools is n ppliction tht llows you to drw on projected imges. By using the interctive pen supplied with

More information

Fig.25: the Role of LEX

Fig.25: the Role of LEX The Lnguge for Specifying Lexicl Anlyzer We shll now study how to uild lexicl nlyzer from specifiction of tokens in the form of list of regulr expressions The discussion centers round the design of n existing

More information

arxiv: v1 [cs.cg] 1 Jun 2016

arxiv: v1 [cs.cg] 1 Jun 2016 HOW TO MORPH PLANAR GRAPH DRAWINGS Soroush Almdri, Ptrizio Angelini, Fidel Brrer-Cruz, Timothy M. Chn, Giordno D Lozzo, Giuseppe Di Bttist, Fbrizio Frti, Penny Hxell, Ann Lubiw, Murizio Ptrignni, Vincenzo

More information

ΕΠΛ323 - Θεωρία και Πρακτική Μεταγλωττιστών

ΕΠΛ323 - Θεωρία και Πρακτική Μεταγλωττιστών ΕΠΛ323 - Θωρία και Πρακτική Μταγλωττιστών Lecture 3 Lexicl Anlysis Elis Athnsopoulos elisthn@cs.ucy.c.cy Recognition of Tokens if expressions nd reltionl opertors if è if then è then else è else relop

More information

Supplemental Notes: Line Integrals

Supplemental Notes: Line Integrals Nottion: Supplementl Notes: Line Integrls Let be n oriented curve prmeterized by r(t) = x(t), y(t), z(t) where t b. denotes the curve with its orienttion reversed. 1 + 2 mens tke curve 1 nd curve 2 nd

More information

OUTPUT DELIVERY SYSTEM

OUTPUT DELIVERY SYSTEM Differences in ODS formtting for HTML with Proc Print nd Proc Report Lur L. M. Thornton, USDA-ARS, Animl Improvement Progrms Lortory, Beltsville, MD ABSTRACT While Proc Print is terrific tool for dt checking

More information

Angles. Angles. Curriculum Ready.

Angles. Angles. Curriculum Ready. ngles ngles urriculum Redy www.mthletics.com ngles mesure the mount of turn in degrees etween two lines tht meet t point. Mny gmes re sed on interpreting using ngles such s pool, snooker illirds. lck

More information

AML710 CAD LECTURE 16 SURFACES. 1. Analytical Surfaces 2. Synthetic Surfaces

AML710 CAD LECTURE 16 SURFACES. 1. Analytical Surfaces 2. Synthetic Surfaces AML7 CAD LECTURE 6 SURFACES. Anlticl Surfces. Snthetic Surfces Surfce Representtion From CAD/CAM point of view surfces re s importnt s curves nd solids. We need to hve n ide of curves for surfce cretion.

More information

Applications of the Definite Integral ( Areas and Volumes)

Applications of the Definite Integral ( Areas and Volumes) Mth1242 Project II Nme: Applictions of the Definite Integrl ( Ares nd Volumes) In this project, we explore some pplictions of the definite integrl. We use integrls to find the re etween the grphs of two

More information

CS311H: Discrete Mathematics. Graph Theory IV. A Non-planar Graph. Regions of a Planar Graph. Euler s Formula. Instructor: Işıl Dillig

CS311H: Discrete Mathematics. Graph Theory IV. A Non-planar Graph. Regions of a Planar Graph. Euler s Formula. Instructor: Işıl Dillig CS311H: Discrete Mthemtics Grph Theory IV Instructor: Işıl Dillig Instructor: Işıl Dillig, CS311H: Discrete Mthemtics Grph Theory IV 1/25 A Non-plnr Grph Regions of Plnr Grph The plnr representtion of

More information

Fall 2017 Midterm Exam 1 October 19, You may not use any books, notes, or electronic devices during this exam.

Fall 2017 Midterm Exam 1 October 19, You may not use any books, notes, or electronic devices during this exam. 15-112 Fll 2017 Midterm Exm 1 October 19, 2017 Nme: Andrew ID: Recittion Section: You my not use ny books, notes, or electronic devices during this exm. You my not sk questions bout the exm except for

More information

9.1 PYTHAGOREAN THEOREM (right triangles)

9.1 PYTHAGOREAN THEOREM (right triangles) Simplifying Rdicls: ) 1 b) 60 c) 11 d) 3 e) 7 Solve: ) x 4 9 b) 16 80 c) 9 16 9.1 PYTHAGOREAN THEOREM (right tringles) c If tringle is right tringle then b, b re the legs * c is clled the hypotenuse (side

More information

Surfaces. Differential Geometry Lia Vas

Surfaces. Differential Geometry Lia Vas Differentil Geometry Li Vs Surfces When studying curves, we studied how the curve twisted nd turned in spce. We now turn to surfces, two-dimensionl objects in three-dimensionl spce nd exmine how the concept

More information

AVolumePreservingMapfromCubetoOctahedron

AVolumePreservingMapfromCubetoOctahedron Globl Journl of Science Frontier Reserch: F Mthemtics nd Decision Sciences Volume 18 Issue 1 Version 1.0 er 018 Type: Double Blind Peer Reviewed Interntionl Reserch Journl Publisher: Globl Journls Online

More information

prisms Prisms Specifications Catalogue number BK7 Wedge, Beam Deviation, deg

prisms Prisms Specifications Catalogue number BK7 Wedge, Beam Deviation, deg Cotings Wedge Steer bems in opticl systems Cn be used in pirs for continuous ngulr djustment T Hving selected n pproprite wedge, it is esy to crete precise bem devition without ffecting other bem prmeters.

More information

PRISMS. Don t see exactly what you are looking for? CVI Laser Optics specializes in prototype to volume production manufacturing!

PRISMS. Don t see exactly what you are looking for? CVI Laser Optics specializes in prototype to volume production manufacturing! PRISMS Mirrors CVI Lser Optics mnufctures lrge selection of high qulity prisms for use in mny pplictions including diverse industril nd scientific uses, lser trcking nd lignment, spectroscopy, nd militry

More information

Engineer To Engineer Note

Engineer To Engineer Note Engineer To Engineer Note EE-186 Technicl Notes on using Anlog Devices' DSP components nd development tools Contct our technicl support by phone: (800) ANALOG-D or e-mil: dsp.support@nlog.com Or visit

More information

Illumination and Shading

Illumination and Shading Illumintion nd hding In order to produce relistic imges, we must simulte the ppernce of surfces under vrious lighting conditions. Illumintion models: given the illumintion incident t point on surfce, wht

More information

Algebra II Notes Unit Ten: Conic Sections

Algebra II Notes Unit Ten: Conic Sections Sllus Ojective: 0. The student will sketch the grph of conic section with centers either t or not t the origin. (PARABOLAS) Review: The Midpoint Formul The midpoint M of the line segment connecting the

More information

If you are at the university, either physically or via the VPN, you can download the chapters of this book as PDFs.

If you are at the university, either physically or via the VPN, you can download the chapters of this book as PDFs. Lecture 5 Wlks, Trils, Pths nd Connectedness Reding: Some of the mteril in this lecture comes from Section 1.2 of Dieter Jungnickel (2008), Grphs, Networks nd Algorithms, 3rd edition, which is ville online

More information

x )Scales are the reciprocal of each other. e

x )Scales are the reciprocal of each other. e 9. Reciprocls A Complete Slide Rule Mnul - eville W Young Chpter 9 Further Applictions of the LL scles The LL (e x ) scles nd the corresponding LL 0 (e -x or Exmple : 0.244 4.. Set the hir line over 4.

More information

Dr. D.M. Akbar Hussain

Dr. D.M. Akbar Hussain Dr. D.M. Akr Hussin Lexicl Anlysis. Bsic Ide: Red the source code nd generte tokens, it is similr wht humns will do to red in; just tking on the input nd reking it down in pieces. Ech token is sequence

More information

Fig.1. Let a source of monochromatic light be incident on a slit of finite width a, as shown in Fig. 1.

Fig.1. Let a source of monochromatic light be incident on a slit of finite width a, as shown in Fig. 1. Answer on Question #5692, Physics, Optics Stte slient fetures of single slit Frunhofer diffrction pttern. The slit is verticl nd illuminted by point source. Also, obtin n expression for intensity distribution

More information