From Perspectivities to Perspective Collineations
|
|
- Samuel Woods
- 6 years ago
- Views:
Transcription
1 Frm erspectivities t erspective Cllineatins Given distinct planes π and π 0 in extended Euclidean space E3, and a pint n neither plane, the assciated ne-pint prjectin with center maps π bijectively nt π 0. That s a simple fact, but frm the standpint f real-wrld ne-pint prjectins such as perspective drawing r phtgraphy, this map, called a perspectivity, is actually a bit strange. T see why, we first review three types f practical, ne-pint prjectins in Figure 1. bject Center (sun) Center bject Image bject Image Image Abve left: Illustratin f a camera bscura frm Sketchbk n military art, including gemetry, frtificatins, and pyrtechnics. Seventeenth century, rigin unknwn, pssibly Italian. Center Abve: Hubble Telescpe prtrait f Jupiter and I, July 24, J. Spencer (Lwell bservatry) and NASA/ESA. Left: Illustratin f the perspective drawing prcess by Albrecht Dürer. Wdcut, Figure 1: Three practical ne-pint prjectins. In the upper left f Figure 1 is a diagram f a camera bscura, r pinhle camera. A light ray frm an bject (the spire f a dmed building) passes thrugh the center f prjectin (a hle in a wall f a darkened rm) and meets the inverted image n the ppsite wall f the rm. The pht itinerary f the light ray is thus bject-center-image. In the upper right f the figure, 1
2 a light ray leaves the center f prjectin (the sun), passes by the bject (Jupiter s mn I), and meets its image (the shadw f I n Jupiter). The shadw itinerary f the light ray is thus center-bject-image. Finally, in the lwer left f the figure, a light ray leaves an bject (the mdel s hand), passes thrugh the image (a perspective drawing f the hand), and meets the center f prjectin (the artist s eye). The perspective drawing itinerary is thus bject-image-center. Figure 2 shws that nt ne, but all three types f practical ne-pint prjectins are invlved in a plane-t-plane perspectivity. π INHLE HTGRAH F CEAN IMAGE F THE FAR DISTANT, EAST-SUTHEASTERN CEAN IMAGE F THE FAR DISTANT, WEST-NRTHWESTERN RAIRIE ERSECTIVE DRAWING F RAIRIE RAIRIE SHADW F EACH EACH West CEAN East π Figure 2: Schematic f a plane-t-plane perspectivity. T highlight the different types f practical prjectins invlved in the perspectivity, we divide the hrizntal plane π int three regins: tw infinite half-planes called the cean and the prairie, and a narrw strip dividing them called the beach. The center f prjectin is directly abve the shreline the bundary between the cean and the beach. The perspectivity prjects the plane π nt the vertical plane π, which meets π in the bundary between the cean and the prairie. The entire plane π is paved with an avenue f initials G fr perspective gemetry. Lking at the dashed line thrugh cnnecting the cean and its image, we see that the itinerary f the assciated light ray is bject-center-image: the pht type. Thus the image f the cean is like a pinhle phtgraph: the initials G are reversed, the cean almst beneath is mapped very high up n π, and the far eastern cean is mapped just abve the hrizn line 2
3 separating the images f the cean and the prairie. Frm the dashed line thrugh cnnecting the beach and its image, we see that the itinerary f the assciated light ray is center-bject-image the shadw type. Thus the image f the beach is essentially an infinitely elngated shadw. Finally, frm the dashed line thrugh cnnecting the prairie and its image, we see that the itinerary f the assciated light ray is bject-image-center the perspective drawing type. Thus the image f the prairie is a perspective drawing n the vertical plane π. The infinite rad f G initials cnverges t a vanishing pint n the hrizn. The strangest and mst interesting part f the image is the neighbrhd f the hrizn line. The hrizn line itself is the image f the line at infinity, r ideal line, in the plane π. Just abve the hrizn lies the image f the far eastern cean, while just belw it lies the image f the far western prairie! Mre generally, as indicated in Figure 2, pints just abve and belw the hrizn cme frm ppsite pints f the cmpass (as applied t an infinite, flat Earth). 3-D letters The exercise f drawing 3-D letters is instructive in relating plane-t-plane perspectivities with perspective cllineatins. Figure 3(a) is a perspective drawing f a 3-D letter Lying n the grund, alng with a pint X which lies in the plane f the upper, gray-shaded face f the L. ur gal is t make a crrect drawing f the pint X which lies in the grund plane directly belw the pint X in space. As a hint, and fr the purpse f ur discussin, Figure 3(b) shws the vanishing pint f the vertical edges f the L, and the vanishing pint f the retreating, hrizntal edges f the L. Finding X given X is like finding A given A, r given ; it exemplifies the basic task invlved in drawing 3-D letters. The pint lies n the hrizn line. The line is the image f the ideal line in E 3 which is incident with bth the upper and lwer planes (frnt and back faces) f the L. X C C X (a) A A (b) Figure 3: Setup f the prblem f cnstructing the image X f X. As is typical when drawing 3-D letters, there are many crrect ways t cnstruct X given X. 3
4 Figure 4 illustrates a particular methd which will be instructive later. Nte in particular that the figure depicts a plane-t-plane perspectivity in space with center relating the upper and lwer planes f the L; that is, the plane f the gray-shaded surface and the grund plane. The picture plane f the figure that is, the plane f the paper is tilted slightly frward in space, s that we see bth vanishing pints and, which are ideal pints in space that represent perpendicular vertical and hrizntal directins (see als Figure 7). Q k j X X l j Draw the line X until it meets the hrizn line at the pint Q. k Draw the line Q. Since X and Q vanish at Q, they represent parallel hrizntal lines, like the tp and bttm f a fence with a fence pst. l The desired pint X lies at the bttm f the fence, that is, n Q. It als lies n the vertical line X, hence X = X Q. Figure 4: Cnstructin f X given X, reasning in 3-D. There are ther plane-t-plane perspectivities implied by Figure 4; fr example the perspectivity that maps the frnt plane f the letter L nt the plane f the paper, r the perspectivity that maps the back plane f the letter L (the grund plane) nt the plane f the paper. The center f these perspectivities is the reader s viewing eye E (nt pictured in Figure 4, but see Figure 7), assuming it is lcated at the crrect viewpint with respect t the page. These perspectivites are like the ne in Figure 2 with center. Since these mappings are nt the plane f the paper, any pint n the page (say X) can represent a pint in the plane f the gray frnt surface f the L, and likewise any pint n the page (say X ) can represent a pint in the grund plane behind the L. Thus we can think f the mapping X X as representing a mapping frm the plane f the paper t itself. This mapping is a perspective cllineatin. Hwever, because this perspective cllineatin invlves the entire plane f the paper, there are sme pint mappings f the type X X frm the frnt plane f the L t the back plane f the L that are a bit mre challenging t the artist s intuitin methd emplyed in Figure 4. Fr example, Figure 5(a) challenges us t find when the pint is given abve the hrizn line. The figure whimsically depicts this pint as being in the sky f the picture. Recall frm Figure 2 that a cmplete plane-t-plane perspectivity invlves shadw prjectin and perspective drawing and a reversed phtgraphic negative. In particular, the pint in Figure 5(a) is like the pints in the sky f the plane π in Figure 2 which belng t the reversed phtgraphic image f the cean part f the plane π. This makes 3-D intuitin harder t apply when finding in Figure 5(a). 4
5 Rather than try t draw r imagine all three planes invlved (the plane f the page and the frnt and back planes f the L) it s easier t just wrk with the plane f the page and sme basic prperties f perspective cllineatins. (Hwever, we discuss the three-planes pint f view in the next sectin.) Let s jt dwn what we have t wrk with in Figure 5(b). First, we have the pint whse image we wish t determine. We draw that in Figure 5(b). Secnd, a perspective cllineatin has a unique line f fixed pints called the axis. In Figure 5(a) the hrizn line is the image f the line at infinity that belngs t the (parallel) frnt and back planes f the L, hence the pints f are fixed. Thus in Figure 5(b) is the axis f the perspective cllineatin. Third, a perspective cllineatin has a special fixed pint called the center. Every pint and its image (such as A A,, and C C in Figure 3(b)) are cllinear with the center, hence the pint is the center, as drawn in Figure 5(b). Furth, a perspective cllineatin is cmpletely determined by its center, its axis, and the image f any nn-fixed pint (such as in Figure 5(b)). That s because a perspective cllineatin maps pints t pints, lines t lines, and preserves intersectins. Nw we re ready t slve fr. (a) (b) Figure 5: Tw ways f envisining the prblem. Figure 6 shws hw we can use the abve prperties t find. Cmparisn with the steps in Figure 4 shws that the tw methds are analgus, but the intuitive reasning is different. In Figure 4 we reasned artistically in terms f spatial visualizatin, while the methd f Figure 6 depends strictly upn the prperties f perspective cllineatins. There is n need t think in terms f real bjects in space, but the cnnectin still remains, as we illustrate in the next sectin. 5
6 j Draw the line ; it meets the hrizn line at the pint R. R k Draw the line R. Since R is fixed (it lies n the axis), the line maps t the line R, hence lies n R. l ut als lies n, hence = R. k j l Figure 6: Cnstructin f given, using the prperties f perspective cllineatins. Thinking in 3-D We can interpret the slutin steps in Figure 6 in terms f 3-D letters in space. Figure 7 illustrates this way f lking at the prblem. A yung reader lks at a versin f Figure 5, which lies in a slanted plane α. The reader s viewing eye is at the pint E (pints and lines utside α are dented with bldface letters). The 3-D letter L lies n a hrizntal plane λ, and the upper (frnt) face f the L lies in the hrizntal plane λ. The ideal pint belngs t all vertical lines, such as the line cnnecting the vertices and f the L. The ideal line belngs t the hrizntal planes λ and λ. The viewer sees the ideal pint as the pint in α, and viewer sees the ideal line as the hrizn line in α. The viewer sees the pint in Figure 5(a) as the image f an ideal pint n, and the viewer sees the pints and as the respective pints and in α. efre discussing the pints and it will be helpful t intrduce sme functin ntatin. We dente three perspectivities as fllws, ne with center and tw with center E: In particular we have : λ λ, E : λ α, Q E : λ α. () =, E () =, Q E ( ) =. We are after the perspective cllineatin : α α, where = Q E 1 E, 6
7 and in particular we want t find = ( ) = Q E 1 E ( ). Nw as shwn in Figure 7, 1 E ( ) =, where λ and, E, and are cllinear. Similarly, () =, where λ and, and are cllinear. Finally, Q E ( ) =, where α and,, and E are cllinear. reader s eye E α (plane f Figure 5) t ideal pint and ideal line t ideal pint t ideal pint t ideal pint λ λ Figure 7: Visualizing the three planes in space. In Figure 7 we can think f a light ray (dashed line) leaving the vertex f the L, piercing the plane α in the pint, and striking the reader s eye E. This is the bject-image-center itinerary f a perspective drawing setup, like the ne in the lwer left f Figure 1. In this case it is reasnable t think f E as the viewing eye f an nlker. n the ther hand, Figure 7 shws a light ray leaving the pint, passing thrugh the back f the reader s eye E, cming ut the pupil, and striking the plane α at the pint! bviusly the characterizatin f E as a persn s eye is nt apprpriate in this case. In fact, this is the bject-center-image itinerary f a pinhle camera, like the picture in the upper left f Figure 1. Anther drawback f Figure 7 is that it is a rather cmplicated methd f lcating given, by cmparisn with the simple methd f Figure 6. Nevertheless, the idea f Figure 7 suggests an interesting interpretatin f the perspective cllineatin, and it reminds us that even simple exercises like drawing 3-D letters can have deeper implicatins. 7
5. Experimental Results
5. xperimental Results Prttype mdels f the duble spherical helix the hemispherical helix studied in Sectins 4.3.2 4.4 were cnstructed measured. Fabricatin f these antennas measurement f their radiatin
More informationREFLECTING ON OUR IDENTITY
REFLECTING N UR IDENTITY Lauren Rbles MYP Visual Art Grade 8 KEY CNCEPT RELATED CNCEPT GLBAL CNTEXT Identity Bundaries, Representatin Identities & Relatinships STATEMENT F INQUIRY Multiple representatins
More informationDispersion is the splitting of white light into its colour components.
Chapter 21 Clurs (A) Dispersin 1. Define dispersin. Dispersin is the splitting f white light int its clur cmpnents. 2. What is the clur that sunlight appears t be? White 3. State the seven clurs in sunlight
More information2018 Print and DPI Annual Competition Rules
Brisbane Camera Grup 'Annual Cmpetitin' takes place in Nvember each year. It's the highlight f the club cmpetitin year and submissin standards are cnsistently high. All graded members are eligible and
More informationMeet the Science Expert
Smithsnian Latin Center Meet the Science Expert DESCUBRA! CREATE-IT POCKET SCIENCE HANDOUTS DESIGN AND BUILD WIND INSTRUMENTS 1. Overview: Wrking with different sized straws and ther materials (see the
More informationBig Kahuna Assembly Instructions
Big Kahuna Assembly Instructins Thank yu fr purchasing a d-it-yurself pergla kit frm Average Je s Pergla Dept. We appreciate yur business, and we are here t help yu in any way pssible. Read this entire
More information31. A light wave travels with a wavelength of 4.0 x 10 m. What is the frequency? (A) Hz (C) Hz (B) Hz (D) Hz
Physics 2204 Unit 4 Review ANSWERS (June 2013) 30. Which is an example f a lngitudinal wave? light wave sund wave radi wave water wave 7 31. A light wave travels with a wavelength f 4.0 x 10 m. What is
More informationDrawing Canvas Word 2007
Drawing Canvas Wrd 2007 This is nt an fficial training handut f the Educatinal Technlgy Center, Davis Schl District The Drawing Canvas... 2 Creating the Drawing Canvas... 2 Shapes... 2 Inserting a Shape...
More informationNational Curriculum Programme of Study:
Natinal Curriculum Prgramme f Study: Cunt in steps f 2, 3, and 5 frm 0, and in tens frm any number, frward and backward. Recall and use multiplicatin and divisin facts fr the 2, 5 and 10 multiplicatin
More informationA4: Color. Light: You can usually any lighting that you wish.
Art 205 A4: Clr Original RAW Shts Due: Crit Date: Requires 2 Ink Jet Prints Munting Crrectly can btain 5 pints extra credit. (50 pints) Objectives: 1. Learn basic clr schemes fr design and aesthetics.
More information3: Community Gathering Space
3: Cmmunity Gathering Space What: 2 part spatial sequence with gathering area fr varius sized grups Entry Zne Prvide an intrductin t the area by establishing a md and character and as well as separating
More informationColourful Stitches. Quick Summer Medallion. 45 x 45 Gyleen X. Fitzgerald Quick Summer Medallion.
Quick Summer Medallin 45 x 45 Clurful Stitches 16 (finished) panel r rphan blck fr center ½ yard, center framing triangles ¼ yard, skinny frame brder 1 ⅔ yard, inside setting triangles 1¼ yard, utside
More informationPhotoVu Digital Picture Frame Service & Repair Guide
PhtVu Digital Picture Frame Service & Repair Guide PhtVu, LLC 2450 Central Ave, #G1 Bulder, CO 80301 USA www.phtvu.cm/supprt Versin: 1.0 Table f Cntents Getting Started... 3 Determine Yur Generatin f PhtVu
More informationFourier Series LABVIEW GUI Documentation
Furier Series LABVIEW GUI Dcumentatin INTRODUCTION The Furier Series GUI is meant t be used as a learning tl t better understand the Furier Series. The user is able t input the amplitude and frequency
More informationUsing the Laser Cutter
Using the Laser Cutter Prerequisites Befre yu will be allwed t use the laser cutter, yu must cmplete these three steps: 1. Yu must have cmpleted the Laser Cutter training at Cyberia 2. Yu must schedule
More informationNote: If using fusible web adhesive to secure stars, prewash all fabric but do NOT use fabric softener.
Made in USA By Dawn Cavanaugh APQS Natinal Educ atin and Service Directr Celebrate summer with this bright, patritic quilt! Use yur favrite methd t secure the stars t lng strips f blue fabric t speed up
More informationANTIOCH UNIVERSITY VIRTIUAL WRITING CENTER
IDENTIFYING AUDIENCE AND PURPOSE As yu mve further int yur research, it can be helpful t step back and name the purpse and audience yu think yur writing will serve. The prcess belw will help yu sift thrugh
More informationProject Information o Simulating Cumulus Entrainment: A Resolution Problem, or Conceptual? o Sonia Lasher-Trapp, UIUC o
Annual Reprt fr Blue Waters Allcatin: Snia Lasher-Trapp, Oct 2016 Prject Infrmatin Simulating Cumulus Entrainment: A Reslutin Prblem, r Cnceptual? Snia Lasher-Trapp, UIUC slasher@illinis.edu Executive
More informationFoam Rocket. Rocket Activity. Objective Students will learn about rocket stability and trajectory with rubber band-powered foam rockets.
Rcket Activity Fam Rcket Objective Students will learn abut rcket stability and trajectry with rubber band-pwered fam rckets. Descriptin Students will cnstruct rckets made frm pipe insulating fam and use
More informationPuget Sound Company Overview. Purpose of the Project. Solution Overview
Puget Sund Cmpany Overview Puget Sund Energy is Washingtn State s largest and ldest energy utility, serving nearly 1 millin electric custmers and mre than 650,000 natural gas custmers, primarily within
More informationTUTORIAL I ECE 555 CADENCE SCHEMATIC SIMULATION USING SPECTRE
TUTORIAL I ECE 555 CADENCE SCHEMATIC SIMULATION USING SPECTRE Cadence Virtus Schematic editing prvides a design envirnment cmprising tls t create schematics, symbls and run simulatins. This tutrial will
More informationSecurity Exercise 12
Security Exercise 12 Asynchrnus Serial Digital Baseband Transmissin Discussin: In this chapter, yu learned that bits are transmitted ver a cpper wire as a series f vltage pulses (a prcess referred t as
More informationFinding your Fantasy: Once Upon a Time... Student Teacher: Andrea Slusarski Co-op Teachers: Darci Wilson (3 rd ) Kelly Vail (2 nd )
Finding yur Fantasy: Once Upn a Time... Student Teacher: Andrea Slusarski C-p Teachers: Darci Wilsn (3 rd ) Kelly Vail (2 nd ) Grade Level: 2 nd & 3 rd Grade Date Taught: April 13 th, 2010 Date Revised:
More informationPAPER SPACE AND LAYOUTS
PAPER SPACE AND LAYOUTS There are tw distinct wrking envirnments in AutCAD namely: Mdel Space and Paper space. Prjects can be develped by either wrking in the mdel space thrugh the use f MVSETUP r PAPER
More informationCyrus Redblock. Kit Inventory
Kit Inventry Cyrus Redblck Left and Right Inner Side Panels Frnt and Back Inner Panels Shelf Panel Base Outer Panel Drawer Left and Right Sides Frnt and Back Drawer pieces Drawer Stp and Tw (2) Drawer
More informationCENTRE FOR DISTANCE EDUCATION ANNA UNIVERSITY CHENNAI GUIDELINES FOR PREPARATION OF MCA PROJECT REPORT
CENTRE FOR DISTANCE EDUCATION ANNA UNIVERSITY CHENNAI 600 025 GUIDELINES FOR PREPARATION OF MCA PROJECT REPORT (Prescribed Frmat and Specificatin) 1. GENERAL: The guideline is intended t prvide brad guidelines
More informationPencil Drawing. Hard 2H H F HB B 2B 4B 6B Soft
This activity is abut learning hw t use ur pencils t create wnderful images like these. Take a lk at a few that All Saints students have dne in the past. (Take a lk at the riginals at the frnt f the rm
More informationGrade 7. National Core Visual Arts Standards. Lesson Assignment (Criteria for Success) Artist/Big Idea
Grade 7 Natinal Cre Visual Arts Standards Lessn Assignment (Criteria fr Success) Artist/Big Idea Dcument Evidence f Mastery (Skills/Techniques) Line/Angle Drawings Creating: VA:Cr1.2.7 - Develp criteria
More informationName: Date: Period: 1. Multi-Genre Character Project
Name: Date: Perid: 1 Multi-Genre Character Prject A multi-genre prject is ne large prject with many different parts. Each part represents what yu knw abut a tpic and extends yur thinking in many ways.
More informationRiverSurveyor S5/M9 & HydroSurveyor Second Generation Power & Communications Module (PCM) Jan 23, 2014
SnTek, a Xylem brand 9940 Summers Ridge Rad, San Dieg, CA 92121-3091 USA Telephne (858) 546-8327 Fax (858) 546-8150 E-mail: inquiry@sntek.cm Internet: http://www.sntek.cm RiverSurveyr S5/M9 & HydrSurveyr
More informationPreLab5 Temperature-Controlled Fan (Due Oct 16)
PreLab5 Temperature-Cntrlled Fan (Due Oct 16) GOAL The gal f Lab 5 is t demnstrate a temperature-cntrlled fan. INTRODUCTION The electrnic measurement f temperature has many applicatins. A temperature-cntrlled
More informationPhotoshop Elements 7 Intermediate: Layout & Design
Phtshp Elements 7 Intermediate: Layut & Design Designing a prject... 2 Preparing pictures fr use in a prject... 2 Creating a new blank dcument... 2 Adding a picture(s) t a prject... 2 Turning n the Ruler/Grid...
More informationPool & Hot Tub Guide
Pl & Ht Tub Guide PERMIT(S) FOR POOLS/HOT TUBS WITH SIDE WALLS > 24 ***** ALL FEES DUE AT TIME OF APPLICATION ***** Building Permit Applicatin. Be aware f any subdivisin restrictins prir t applicatin.
More informationELECTRICAL MEASUREMENTS
Physics Department Electricity and Magnetism Labratry ELECTRICAL MEASUREMENTS 1. Aim. Learn t use measuring instruments: Digital multimeter. Analg scillscpe. Assembly f simple elementary circuit. Cllectin
More informationPulse Width Modulation (PWM) Cornerstone Electronics Technology and Robotics II
Pulse Width Mdulatin (PWM) Crnerstne Electrnics Technlgy and Rbtics II Administratin: Prayer PicBasic Pr Prgrams Used in This Lessn: General PicBasic Pr Prgram Listing: http://www.crnerstnerbtics.rg/picbasic.php
More informationFlattering Posing - Avoid poses that place the subject in awkward or unnatural positions.
Psing Psing shuld be apprpriate fr age, sex, and bdy type f the individual(s) phtgraphed. Psing shuld be designed t enhance attributes f the subject and minimize flaws. Lighting Bdy Angle Shulders shuld
More informationEDISON. The Mystery of the Missing Mouse Treasure. The truth turns out to be far more amazing.
EDISON The Mystery f the Missing Muse Treasure Tw unlikely friends build a vessel capable f taking them t the bttm f the cean as they search t find a missing treasure The truth turns ut t be far mre amazing.
More informationProcess Gain and Loop Gain
Prcess Gain and Lp Gain By nw, it is evident that ne can calculate the sensitivity fr each cmpnent in a cntrlled prcess. Smetimes, this sensitivity is referred t as a gain. The cnfusin is understandable
More informationSINGER FUTURA TM Holiday Banner
SINGER FUTURA TM Hliday Banner Have fun decking the halls with this festive banner! It s s simple t make the HyperFnt sftware and yur SINGER FUTURA machine. Create the base applique right in yur embridery
More informationINSTRUCTION BOOKLET (PUZZLES BY NIKOLA ZIVANOVIC)
LMI DECEMBER PUZZLE TEST PUZZLES & CHESS -2. DECEMBER 200. INSTRUCTION BOOKLET (PUZZLES BY NIKOLA ZIVANOVIC) SUBMISSION: http://lgicmastersindia.cm/m2002p 0 PUZZLES 70 MINUTES POINTS TABLE CHESS BATTLESHIPS
More informationWhat your Board Should look like!
What yur Bard Shuld lk like! Fr almst every science fair prject, yu need t prepare a display bard t cmmunicate yur wrk t thers. In mst cases yu will use a standard, three-panel display bard that unflds
More informationThe UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Yu will learn the fllwing in this lab: The UNIVERSITY f NORTH CAROLINA at CHAPEL HILL Cmp 541 Digital Lgic and Cmputer Design Prf. Mntek Singh Fall 2016 Lab Prject (PART A): Attaching a Display t the Prcessr
More informationASSEMBLE ALUMINUM TOOLBOX
ASSEMBLE ALUMINUM TOOLBOX INTRODUCTION In this lessn, yu will assemble an aluminum sheet metal tlbx using rivets. Yu will start with a kit that includes pre cut and pre frmed aluminum tlbx panels. This
More informationThis app uses callas pdftoolbox server as the imposition engine and consequently you have to have that program installed on your Switch server.
Autmatic impsitin Page 1/8 Autmatic impsitin Descriptin Autmatic impsitin will d the mst cmmn impsitins fr yur digital printer. It will autmatically d flders fr A5, A4 r US Letter page sizes in either
More information6.1 Angles in Standard Position In Quadrant 1.notebook May 24, 2015
Unit 6 Trignmetry 6.1 Angles in Standard Psitin in Quadrant 1 1 6.1 Trignmetry: Angles in Standard Psitin Outcmes 6.1, 6.2 & 6.6 Determine & sketch the angle in standard psitin given a pint P(x, y) n the
More informationRectifiers convert DC to AC. Inverters convert AC to DC.
DT23-3 Inverter Ntes 3 January 23. The difference between Rectifiers and Inverters Rectifiers cnvert DC t AC. Inverters cnvert AC t DC. 2. Uses f Inverters Battery Backup. Batteries stre DC. Many appliances
More informationHands-Free Music Tablet
Hands-Free Music Tablet Steven Tmer Nate Decker Grup Website: steve@wasatch.cm milamberftheassembly@yah.cm http://www.cs.utah.edu/~ndecker/ce3992/ Abstract The typical musician handles a great deal f sheet
More informationPhysics 30 Lesson 9 Optics Thin Lenses
Reer t Pearsn pages 677 t 68. Physics 30 Lessn 9 Optics Thin Lenses The stuy lenses is very similar t that curve mirrrs. Hwever, while mirrrs invlve relectin, lenses invlve reractin. In act, r lenses there
More informationBigMouth
http://www.scaryguys.cm/bigmuth.htm BigMuth Yu're walking dwn a dark path, and cme upn an area cvered with cam net. On ne wall it lks like a table with a skull perched n the edge. Just cam net hanging
More informationTake Along Sewing Tote
Take Alng Sewing Tte This great tte will hld lts f supplies fr yur take alng prjects. Specifically designed fr English Paper Piecing, any small prject will fit int this tte. Just thrw it in yur purse and
More informationCascading Skirt Pattern
Cascading Skirt Pattern Fr this pattern yu will need: 1/3 yard f well draping fabric. Swimwear, dance fabrics, and very stretch knits are the perfect fabrics fr this pattern s style. (Yu can use ld T-shirts
More informationAppendix D. Photography
Appendix D Phtgraphy 1 I. Taking Phtgraphs Taking phtgraphs is a required NWCA field activity that prvides an imprtant visual recrd f sampling activities at each site. Phtgraphs are taken with a digital
More informationDXF2DAT 3.0 Professional Designed Computing Systems 848 W. Borton Road Essexville, Michigan 48732
Prgram Infrmatin 1 DXF2DAT 3.0 Prfessinal Designed Cmputing Systems 848 W. Brtn Rad Essexville, Michigan 48732 Cntact: (989) 892-4376 website: http://www.famwrk.net General Infrmatin: inf@famwrk.net Technical
More informationWaves Unit / Mechanical Waves Sub-Unit
Waves Unit / Mechanical Waves Sub-Unit 5.1.1 Oscillatins - time fr ne scillatin - number f scillatins per secnd Equatin Pendulum Mass n a Spring PRACTICE Regents Physics 1. A pendulum is timed as it mves
More informationSARMAP RELEASE NOTES. Version: 7.0 (July 2016) rpsgroup.com
SARMAP RELEASE NOTES Versin: 7.0 (July 2016) 55 Village Square Dr. Suth Kingstwn, RI 02879 Tel: (401) 789-6224 Fax: (401) 789-1932 Email: MapSupprt@ Table f Cntents Table f Cntents...ii 1 Intrductin...
More informationa) Which points will be assigned to each center in the first iteration? b) What will be the values of the k new centers (means)?
CS 378 Cmputer Visin Prblem set 2 Out: Tuesday Sept 22 Due: Mnday Oct 5, by 11:59 PM See the end f this dcument fr submissin instructins. I. Shrt answer prblems [30 pints] 1. Suppse we are using k-means
More informationLab 1 Load Cell Measurement System
BME/ECE 386 Lab 1 Lad Cell Measurement System GOALS Lab 1 Lad Cell Measurement System 1) Build and test a lad cell amplifier. 2) Write an Arduin prgram t: a. Acquire data frm a lad cell amplifier b. Cmpute
More informationAppendix M Trellis Type Shade Structure Design Guide
Residential Design Guidelines fr Marley Park 178 Appendix M Trellis Type Shade Structure Design Guide Trellis Type Shade Structures: Trellis Type Shade Structures are typically cnstructed with pen trellis
More informationTROUBLESHOOTING GUIDE
TROUBLESHOOTING GUIDE Dcument revisin 1.3 Last revised: December 6, 2017 Recn Wireless Blckage and Flw Mnitr Trubleshting Guide 2014-2017 Intelligent Agricultural Slutins All Rights Reserved. Recn Wireless
More informationFreading for Kindle Fire Using the SlideME app.
Harvard Public Library www.harvardpubliclibrary.rg Freading fr Kindle Fire Using the SlideME app. Freading is an e-bk cllectin, available t Harvard Public Library cardhlders, that ffers tens f thusands
More informationA2: Aperture, DOF, & Focus
Art 205 A2: Aperture, DOF, & Fcus Original RAW Shts Due: Crit Date: Requires 2 Ink Jet Prints (50 pints) Objectives: 1. T understand hw apertures like f-16 & f-22 have a large DOF r range f fcus. 2. T
More informationAccuBuild Version 9.3 Release 05/11/2015. Document Management Speed Performance Improvements
AccuBuild Versin 9.3 Release 05/11/2015 Dcument Management Speed Perfrmance Imprvements The entire dcument management system and security system design was retled which shuld result in majr speed imprvements
More informationHospital Task Scheduling using Constraint Programming
Hspital Task Scheduling using Cnstraint Prgramming Authr: Chaman Chahal Supervisr: Dr. P. Bse, Schl f Cmputer Science Organizatin: Carletn University Curse: COMP4905 Date: Dec. 11, 2012 1 Abstract Hspitals
More informationLast update: December 26, English Translation DRAFTS of Asian Rules by Eric Wu. Contents
WXF r Asia rule Name:Lee JiHai (The Cmmittee f Referees Hng Kng Chinese Chess Assciatin) Lcatin:Hng Kng Last update: December 26, 2005 English Translatin DRAFTS f Asian Rules by Eric Wu. Cntents Intrductin
More informationFlood Snakes and Ladders. Facilitators notes
Fld Snakes and Ladders Facilitatrs ntes May 2011 Fld Snakes and Ladders Facilitatr s Ntes This guide tells yu everything yu need t knw t run the game successfully. It cvers: 1. Setting up the game 2. Intrducing
More informationf f d o FIGURE 1 - Light ray diagram
Lab 10 Thin Lenses What Yu Nee T Knw: The Physics Frm last week s lab, Reflectin an Refractin, yu shul alreay be familiar with the fllwing terms: principle axis, fcal pint, fcal length, f, cnverging lens
More informationSpring 06 Assignment 3: Robot Motion, Game Theory
15-381 Spring 06 Assignment 3: Rbt Mtin, Game Thery Questins t Rng Yan(yanrng@cs.cmu.edu) Out: 2/21/06 Due: 3/7/06 Name: Andrew ID: Please turn in yur answers n this assignment (etra cpies can be btained
More informationMath 3201 Unit 8: SINUSODIAL FUNCTIONS NAME: Up until now we can measure angles using degrees.
Math 0 Unit 8: SINUSODIAL FUNCTIONS NAME: Sectin 8.: Understanding Angles p. 8 Hw can we measure things? Eamples: Length - meters (m) r ards (d.) Temperature - degrees Celsius ( C) r Fahrenheit (F) Hw
More informationApplication of Percents
Grade 7 Mathematics, Quarter 3, Unit 3.1 Applicatin f Percents Overview Number f instructinal days: 15 (1 day = 45 60 minutes) Cntent t be learned Cnvert between different frms f ratinal numbers (psitive
More informationAmerican Association of State Highway and Transportation Officials
American Assciatin f State Highway and Transprtatin Officials Please save and send as a wrd file. Yu can attach a map in PDF r JPG with the applicatin t usrutes@aasht.rg (M.Vitale) An Applicatin frm the
More informationProducing Research Posters
Dr Keith E. Fildes 21/23 Octber 2014 (with acknwledgments t Dr Lyuba Albul, CARR) Objectives This sessin will cver: The purpse f psters What shuld be included Design cnsideratins Getting started The fllw-up
More informationE-Jobsheet Tablet Application Functionality
E-Jbsheet Tablet Applicatin Functinality The e-jbsheet applicatin has been created fr Truck Service Prviders (TSP) in rder fr their admin staff and fitters t handle all types f wrk via a mbile platfrm
More informationSelecting Yo r Guitar Notes on the First String: Introducing E Acoustic Guitars and Electric Guitars The Note E with Chords Tuning Your Guitar
Selecting Yur Guitar... 5 Steel Strings and Nyln Strings Acustic Guitars and Electric Guitars... 7 aring fr Yur Guitar Tuning Yur Guitar... 9 Tuning with the Ds Tuning withut the Ds Hw t Hld Yur Guitar...
More informationFor as long as there have been people trying to find their way, there have been stars to guide them. Stars dance in the heavens weather we see them
Fr as lng as there have been peple trying t find their way, there have been stars t guide them. Stars dance in the heavens weather we see them there r nt. They warm the darkness f the night and fill us
More informationIB Visual Arts Summer Work Year 1 (HL & SL)
IB Visual Arts Summer Wrk Year 1 (HL & SL) Cngratulatins n beginning yur jurney int the IB Visual Arts Curse. There are a few things I wuld like yu t knw befre yu get started n yur summer wrk. - Making
More informationRIG SOLAR FILM. High quality clear 48 gauge Polymer material \V;th excellent transmission qualities.
... a. Ul -'" '" c / RIG SOLAR FILM Fr ver 25 years, Thusand Oak Optical has manufactured the mst ppular white lightfilters in the wrld. Nw with the intrductin f the R-G slar film, ur traditin f excellence
More informationMpressive Threadz Studio
Mpressive Threadz Studi Sewing Schl Prject # 1 Drafting Yur Six- gre Skirt and Fitting It The six gre skirt is easy t draft, easy t sew, and easy t fit. It has a gentle flare t it and it flatters all bdy
More informationWiFi Lab C. Equipment Needs:
WiFi Lab C Event Objective: Teams will cnstruct an antenna prir t the turnament that is designed t transmit a signal at 2.4 GHz and cmplete a written test n the principles f electrmagnetic wave prpagatin.
More informationArt of Work Look & See: Who do you want to be? Utah Museum of Fine Arts Educator Resources and Lesson Plans Fall 2016
bjects frm the UMFA Educatin Cllectin Art f Wrk Lk & See: Wh d yu want t be? Utah Museum f Fine Arts www.umfa.utah.edu Educatr Resurces and Lessn Plans Fall 2016 American Suthwest Bear Kachina Dll Cttnwd
More informationECE 3829: Advanced Digital System Design with FPGAs A Term 2017
ECE 3829: Advanced Digital System Design with FPGAs A Term 2017 Lab 2- VGA display and Light Sensr interface Reprt due at start f class Friday September 15 th Use the prvided Ambient Light Sensr mdule
More informationDance Savvy Workshop Template
Dance Savvy Wrkshp Template Facilitatrs: Gal: Length: Setup Needs: One YBCA Staff member, ne Guest Expert (The gal f the wrkshp shuld be tailred t yur specific desired utcmes, fr example:) T explre cntemprary
More informationAPPENDIX B: DESIGN RATING SURVEYS (DRS)
APPENDIX B: DESIGN RATING SURVEYS (DRS) 1. Is the device handheld? Yes, it s handheld N Nt Explicitly Stated MILK FROTHER DRS (if nt handheld) 2. If the device is NOT handheld, what des it lk like? it
More informationOperating Instructions
TC 60/8 THERMOCOMPUTER TC 60/8 temp / time s s temp / time k start stp Operating Instructins Cntents General Infrmatin...1 Security Advice...1 Firing Curves...1 Typical Firing Curves...2 Entering a Firing
More informationSpring 06 Assignment 3: Solution
15-381 Spring 06 Assignment 3: Slutin Questins t Rng Yan(yanrng@cs.cmu.edu) Out: 2/21/06 Due: 3/7/06 Name: Andrew ID: Please turn in yur answers n this assignment (etra cpies can be btained frm the class
More informationidcv Isolated Digital Voltmeter User Manual
www.akcp.cm idcv Islated Digital Vltmeter User Manual Help Versin updated till firmware SP446 Cpyright 2011, AKCess Pr Limited Prvided by fficial AKCP-Distributr Didactum https://www.didactum-security.cm/en/
More informationExcel Step by Step Instructions Creating Lists and Charts. Microsoft
Infrmatin Yu Can Enter in a Wrksheet: Labels: Any type f text r infrmatin nt used in any calculatins. Labels are used fr wrksheet headings and make wrksheets easy t read and understand. Labels can als
More informationWS-400 BASE STATION FOR WIRELESS INTERCOM WITH FOUR TX/RX MODULES USER MANUAL
WS-400 BASE STATION FOR WIRELESS INTERCOM WITH FOUR TX/RX MODULES USER MANUAL Issue February 2011 ASL Intercm BV DESIGNED AND MANUFACTURED BY: ASL INTERCOM BV ZONNEBAAN 42 3542 EG UTRECHT THE NETHERLANDS
More informationLab 1 Load Cell Measurement System (Jan 09/10)
BME/ECE 386 Lab 1 Lad Cell Measurement System GOALS Lab 1 Lad Cell Measurement System (Jan 09/10) 1) Test the lad cell amplifier. 2) Write an Arduin prgram t: a. Acquire data frm a lad cell amplifier b.
More informationDesktop Teller Exception User Guide
Desktp Teller Exceptin User Guide Jammed Dcuments If a dcument jams during the scanning prcess, the scanner will stp, and a message bx will display a Device Errr Message, as shwn belw: Click OK t allw
More informationManual Zeiss Axio Zoom.V16 microscope and ZEN 2 Pro software
Manual Zeiss Axi Zm.V16 micrscpe and ZEN 2 Pr sftware 15-9-2015 Fred Hartjes EMS 3 Caxial illum. Ring illum. Starting up Pwer n Actuate the knb n the EMS 3 cntrl unit Switch n the caxial illuminatin Switch
More informationTownship of Derry. Dauphin County, Pennsylvania. Residential Deck Addition Submittal Guide and Construction Fact Sheet
Twnship f Derry Dauphin Cunty, Pennsylvania Residential Deck Additin Submittal Guide and Cnstructin Fact Sheet The text and illustratins included in this guide represent tables and illustratins frm the
More informationSVT Tab and Service Visibility Tool Job Aid
Summary This Jb Aid cvers: SVT Tab Overview Service Visibility Tl (SVT) Area Overview SVT Area: Satellite Mdem Status (Frm Mdem) Clumn SVT Area: Satellite Mdem Status (Frm SMTS) Clumn SVT Area: Prvisining
More informationOperating Instructions
TC 40 THERMOCOMPUTER TC 40 start stp Operating Instructins Cntents General Infrmatin...1 Security Advice...1 Firing Curves...1 Typical Firing Curves...2 Entering a Firing Curve...2 Checing the Prgramme
More informationYear 11 Visual Arts Assessment Task 2, 2018
CAMDEN HIGH SCHOOL Traditin Opprtunity Innvatin Success Year 11 Visual Arts Assessment Task, 018 TOPIC: Artmaking Task - Visual Arts Prcess Diary () and Bdy f Wrk (BOW)- Issues and Theries SUBMISSION REQUIREMENTS:
More informationCUSTOMER PORTAL. Floorplan Management
CUSTOMER PORTAL Flrplan Management FLOORPLAN ANALYTICS The flrplan analytics area displays flrplans yu have uplad t the prtal (if yu haven t yet upladed a flrplan please cntact ur supprt department). Frm
More informationBanner pocket v3 Page 1/7. Banner pocket v3
Banner pcket v3 Page 1/7 Banner pcket v3 Descriptin Banner pcket will help yu get the printed sheets arranged in the way yu need fr attaching the frnt and back side pckets tgether. It will crp ne sides
More informationTen-Tec Model RX-366 Subreceiver 565/566 Subreceiver Installation and Operation Manual-74467
Ten-Tec Mdel RX-366 Subreceiver 565/566 Subreceiver Installatin and Operatin Manual-74467 Tls required: Sldering irn r heat gun (fr shrinking heat shrink tubing) Number 1 Phillips screw driver Number 2
More informationTC 60 THERMOCOMPUTER TC 60. prog. start stop. Operating Instructions
TC 60 prg start stp THERMOCOMPUTER TC 60 h C/h C Operating Instructins Cntents General Infrmatin...1 Security Advice...1 Firing Curves...1 Typical Firing Curves...2 Entering a Firing Curve...2 Checing
More informationPHYS 102 Quiz Problems Chapter 17 : Sound Waves Dr. M. F. Al-Kuhaili 1. (TERM 001) 2. (TERM 001) 3. (TERM 002) 4. (TERM 002) 5.
PHYS 102 Quiz Prblems Chapter 17 : Sund Waves Dr. M. F. Al-Kuhaili 1. (TERM 001) A mving train is blwing a whistle at 500 Hz. An bserver at rest hears the sund at 480 Hz. What is the speed f the train,
More informationMicrosoft PowerPoint 2007
Micrsft PwerPint 2007 Finding Presentatins n the Web Open the Internet and g t http://www.ggle.cm Click n Advanced Search. Enter wrds r phrases t describe desired results. On the File Frmat line, click
More information