Computer assisted assembly and rendering of solids 作者：GW Romney 摘要：The objective of the paper is to describe a technique that produces shaded renderings of solids; and to describe an assembly procedure which may be used to assemble representations of 3-D objects in such a way that they can be photog
COMPUTER ASSISTED ASSEMBLY AND RENDERING OF SOLIDS by Gordon wilson roam y A thesis submitted to the faculty of the University of Utah in partial fulfillment of the requirements for the degree of D。 ctor of phi1 sophy Department of Electrical Engineering University of utah August 1969 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission This Thesis for the Doctor of philosophy Degree by Gordon Wilson Romney has been approved July 1969 Chairman,, supervisory Conunlttee 2. Reader, Supervisory Committee ∠!线 Reader, Supervisory mittee Reaper, Supervisory Committee Reader, Supervisory Committee a r Major Departmen 七 Dean, Graduate Schoo Reproduced with permission of the copyright owner. Further reproduction prohibited without permission ACKNOWLEDGMENTS I thank Dr. David c, Evans for the initial inspiration to render shaded objects by using a point source of illumi- nation located at the eye-point and for suggesting that the di. splay device be raster driven←工aLs。, appreciate his sponsorship of this research as the principal investigator of an ARPA contrad七。 To my deceased colleague chris Wylie I express nmy grat itude for his creativity. The initial algorithm upon which this thesis is based was developed in close association with chris Dr, Ivan E. Sutherland provided the impetus that brought thi8 work to its箕ina]Eoxm,8￠x饥e1ana]y8i8 of the esu⊥七 s has been a most va1uab1econ七buon. fo hin工ex press my thanks for his friendship and inspiration I also appreciate the hours contributed by Professor homas c。 Stockham and professor r。bext卫 Stephenson with regards to the recording technques Behind the scenes of an endeavor such as this are the faithful and diligent colleagues. To Gary s. Watkins and Michael Archuleta I extend my thanks for their friendship and diligence that made this work possible. They are two of the most creative individuals with whom I have ever associated and many of the ideas expressed in this work must be accredit- edt。them。 Most importantly, I thank my sweet wife, viki, and chil- dren for their patience, understanding and inspiration. Some- day, perhaps, I can make up to them the nights spent alone Reproduced with permission of the copyright owner. Further reproduction prohibited without permission TABLE OF CONTENTS PAGE ACKNOWLEDGMENTS 1飞 LIST OF工 LLUSTRAT工oNS XL ABSRACL 工。工 ntroduction:.。。 I1 Sampling processes I2 Computer-Generated Images I3 visible Surface Algori thms 工。4 bject De￡ inition Problems I。5 hesis objective 10 II。 Rendering·· 12 工工。1 Introduction,,,。 12 工T。2 Data de￡ inition 15 工I3 Geometry。·,···· 19 工工.3.1A3- D Projective Transformation.1 I。32c1 upping 23 II.3.3 Rounding 24 I工。3.4 Sampling Points 27 I工.4S。 rting 30 工。4.1y-S。rt 33 工T。4。2X一s°Pt 41 II. 5 Depth Computation 45 I工,51 Depth Interp。1 ation Equation 45 II. 5.2 Rendering Process Sequence 48 工王。5。3Vsib1 Surface Procedure 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission SECTION PAG它 工。6 Shader 58 工。6.]" Ad hoc" Shading,,,,,, 59 工6.2 Segment processing。·: 59 II.7 Experimental Results 62 工r7.1 Rendering Memory Requirement· 62 r工.72 Rendered object8 66 工工.73Px。 jection E1 ane Resolution· 81 工工, Assemb1y 83 工工工。1工 ntroduction 83 III2 Primitive Objects 86 IIT.3Matx1 x fransformations。。。 99 III.3.1 object Update Matrix 89 工工.32 Display C。 ordinate System, 90 I工330 bject centr0 9工 工工工3,4 Maintaining the Orthogona1 Quality 91 工了。3.5A11owea3a1 s Transformations92 工T工4Da七aDen七n 95 工了T。4·1Da七 a structure。。。。 95 工工工42ob」 ect Header and data 98 工工工.4.3 object Grouping 100 工r5 Language 102 工工。51 A Light Button Language,。。102 工工·5·2 Operand Queue·,· 103 工工。530 eration。ueue 104 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission SECTION PAGE 工Ir。5。4 state Diagram,·······104 工工工.6 Critique。。。。。 109 V。 Future Research 112 V。卫 rojection·····。。。。。: 116 1 Parallel versus Perspective Projection 116 v2 Projective Transformation 118 v 3 Projection-A 3-D Trans formation 123 Equivalent Projective Trans formations 125 VI. Shading 130 VT。1工 introduc七in 130 V工.2eoxy,。·· 132 V工。3Rue8,,。,。,,。。,,,,,。134 VT。3。1CosθRuLe 134 VI.3.2 Cos 0/R- Rule 135 VI.3.3 COS 0/R Rule 135 V.3.4cosθ/R-Rule 135 V工。4he" Ad hoc"Rule;.,。。;。 137 VI 5 Intensity Normalization . 138 V工工。 Recording 143 VI工.1 Introducti 143 VII.2 Recording Procedure 145 VII.3 Color and color control 148 V工了。3。1co1。2 148 VT工3。2co1 or con七o1 150 VI。4 Tone Control 151 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission SECTION PAGE VII5Fi1 m calibrati。n。, 153 VII。6Arec。 mputer Rendering8Ha1tone 155 VT工。7卫 ransfer characteristics。,。 156 Vr工8 Recording Problems·:。 160 VII.8.I -Axis Noise 160 VII.8.2 Z-Axis Amplifier Recovery 161 VII.8.3 Edge Sharpness 161 VI工.8。4Ium⊥ nescence saturat⊥on 161 L⊥ st of references 163 APPENDIX A. Depth Linear Interpolation Equation APPENDIX B·工 ntensity Equa七ion 174 B.1 COS 0/ R- Intensity Rule 174 B2 Orthographic Projection Intensity Rule 177 3 Intensity Iinear Interpolation Equation 178 B.4工 crement1工 ntensity Equation 180 APPENDIX C. Matrices 181 C1 Rotation 182 c。29rans1 atior 183 C。3 Rotation and丌ans1 ation 183 C4MoLd卫 ans formation 184 c 5 Centroid Determination 8 c.6 Centroid De七 ermination a￡ter Mold frans￡ ormation. 1B5 vi且 Re produced with permission of the copyright owner. Further reproduction prohibited without permission SEcr工oN PAGE APPENDIX D. Computed Surfaces,·· 187 Dl Grid Approximation to Curved Surfaces 187 D2 Sphere 188 D 3 Cylinder 191 4 Donut 193 5 Ramp 194 D6 Probability surface 196 APPEND工XE。 Assembly Operators and commands 199 El Operators 199 E。1.1A88i9 199 B。1.2 Center 200 E。1。3co1or 200 E.l.4 Copy 200 。1。5Fe七ch 201 B。1。6 Ident￡ 201 E。1.7 Intensity 201 E。1。8M。16 202 E。1。9Nam 203 E。1,10 New Pic七uxe 203 11 Picture 203 E。1·12 Rende 203 E1·13R。tate 204 E。1.14sav 204 E。1·159ime 205 viii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission