Measurement Of Free-formed Surfaces

How to measure and describe Free-Formed Surfaces Measurement of free-formed surfaces (2008-10-23/30) Graphic ScienceⅡ

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Measurement and description of free-formed surfaces １．Measurement of free-formed surfaces １．１ Moire fringe method １．２ SPG: Stereo Photogrammetry(立体写真計測法) １．３ Three dimensional degitizer

２．Description of free-formed surfaces ２．１ Space curve ２．２ NURBS (Non-Uniform Rational B-Spline) ２．３ Description and generation of surfaces ２．４ Application 2

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１．Measurement of free-formed surfaces １．１ Moire Fringe Method １．１．１ Principle １．１．２ Moire fringe contour １．１．３ Object’s shape from Moire fringe １．１．４ Experimental results

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Surface representation with Moire fringe

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Moire fringe dark 暗

L

暗

L

bright 明 dark

明 bright

暗 dark 暗 bright 明 dark d grid 格子定数 interval

Moire fringe produced with two 二枚の回折格子によるモアレ縞 diffraction grids

L ≒ d/……………(1) 5

light source

screen

Moire fring

camera bright stripe dark stripe Geometric relations in Moire measurement

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 1 

 , d     1 s

 2 

 n 

2 d  2 s

n d   n s

(2)

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light source

screen

lens image plane intersection between the n-th fringe and the grid’s shadow

Distance between the Moire fringe and the screen, n 8

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light source 1

light source 2

screen camera

Moire fringe pattern obtained from the experiment

Experimental set up

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(a) contours

(b) sections

(c) improved Moire methods

Difference of the measures obtained from the Moire and the stereo-photogrammetry methods 10

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三角測量①

三角測量②

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三角測量から三次元計測へ

１．Measurement of free-formed surfaces １．2 Stereo-photographic measurement １．2．１ Principle １．2．２ Application

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x  ( a1 X  a2Y  a3 ) /(a7 X  a8Y  1) y   ( a4 X  a5Y  a6 ) /(a7 X  a8Y  1) 15

xi  (a1 X i  a2Yi  a3 ) /(a7 X i  a8Yi  1) yi  (a4 X i  a5Yi  a6 ) /(a7 X i  a8Yi  1) 16

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rc1  xc1  t1 ( xc1  xc1 ) rc 2  xc2  t2 ( xc2  xc 2 )

xs  rc1  rc 2 17

  t a ( xoa   xsa ) roa  xoa   tb ( xob   xsb ) rob  xob

xo  roa  rob

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Conclusion The minimum numbers of markers necessary for the stereo-photogrammetry are; More than and

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fiducial markers

control markers

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Measurement of the femoral surface of human knee (大腿骨曲面の測定例) Check the numbers of the fiducial and control markers

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Measurement of the cartilage thickness of the human patellar surface 1) Measure the patellar surface 2) Dissolve the cartilage with a regent (薬品） 3) Measure the surface without cartilage

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Measurement of the cartilage thickness of the human patellar surface (膝蓋骨軟骨厚の測定例) Check the numbers of the fiducial and control markers

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１．Measurement of free-formed surfaces １．3 Three dimensional (3D) digitizer １．3．１ Terminology １．3．２ Contact type digitizer １．3．3 Non-contact type digitizer

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１．3．２ Contact type digitizer dialgauge①

Prototype of digitizer by Wismans (1980)

specimen

dialgauge③

dialgauge②

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１．3．２ Contact type digitizer Application to archeology

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１．3．3 Non-contact type digitizer (Laser Scanner)

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Measurement of a swine knee joint surface

Knee joint surface of a swine (豚)

A 3D laser scanner

The number of data points: 11731

Surface reconstruction with polynomial B-spline 28

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Reconstruction of a swine knee joint surface

polynomial（7th order）

Fourier series （11th order）

object surface

reconstructed surface

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Object’s shape measurement with a laser scanner and its reconstruction ① dice

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Object’s shape measurement with a laser scanner and its reconstruction ② mouse with a cord winding around

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Object’s shape measurement with a laser scanner and its reconstruction ③ hands

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Object’s shape measurement with a laser scanner and its reconstruction ④ guess what it is

???

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レポート課題 三角測量の原理を簡単にまとめよ（１頁）

Assignment Submit a short report explaining about the principle of a triangular surveying（A4１page）

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