Measurement of Space Plane Angle Based on Concentric Circle Mark

Fig. 1. Diagrams of relationship between object and image. (a) Intersection points of space straight line and marks; (b) intersection points of straight line image and mark images

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Fig. 2. Flow chart of measurement scheme

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Fig. 3. First simulation diagrams.(a) Simulated objects to be measured; (b) images of marks on object to be measured; (c) partial vanishing points

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Fig. 4. First simulation diagrams. (a) Simulated objects to be measured; (b) Images of marks on object to be measured; (c) partial vanishing points

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Fig. 5. Pictures taken practically. (a)(b) Plane images to be measured; (c)(d)images of marks on plane to be measured

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Table 1. Data of first simulation experiment
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Table 1. Data of first simulation experiment
Normal vector Radius /pixel Rotation matrix Translation matrix Theoretical value /(°) Simulation result /(°)
[ $\begin{matrix} \begin{matrix} 1 & 1 & 1 \end{matrix} \end{matrix}$ ][ $\begin{matrix} \begin{matrix} 0 & 0 & 1 \end{matrix} \end{matrix}$ ] 10, 7 $\begin{matrix} [\begin{matrix} 0 & - 1 & 0 \\ - 0.996 & 0 & 0.087 \\ - 0.087 & 0 & - 0.996 \end{matrix}] \end{matrix}$ [ $\begin{matrix} \begin{matrix} - 20 & - 20 & 35 \end{matrix} \end{matrix}$ ] 125.264 54.736

Table 2. Data of second simulation experiment
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Table 2. Data of second simulation experiment
Normalvector Radius /pixel Rotationmatrix Translationmatrix Theoreticalvalue /(°) Simulationresult /(°)
[ $\begin{matrix} \begin{matrix} 1 & 1 & - 1 / 2 \end{matrix} \end{matrix}$ ][ $\begin{matrix} \begin{matrix} 0 & 0 & 1 \end{matrix} \end{matrix}$ ] 16, 8 $\begin{matrix} [\begin{matrix} 0.075 & - 0.996 & - 0.044 \\ - 0.863 & - 0.087 & 0.499 \\ - 0.500 & 0 & - 0.866 \end{matrix}] \end{matrix}$ [ $\begin{matrix} \begin{matrix} - 80 & - 90 & 140 \end{matrix} \end{matrix}$ ] 70.529 109.471

Table 3. Experimental results

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Table 3. Experimental results

Number ofexperiments	Standardvalue /(°)	Measuredvalue /(°)	Absoluteerror /(°)	Relativeerror /%
1	64.25	63.83	0.42	0.658
2	79.45	79.84	0.39	0.488
3	91.45	91.73	0.28	0.305
4	104.05	104.59	0.54	0.516
5	114.90	114.32	0.58	0.507
6	138.70	138.42	0.28	0.202

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Jingfa Lei, Zhiqiang Chen, Miao Zhang, Yongling Li, Hong Sun. Measurement of Space Plane Angle Based on Concentric Circle Mark[J]. Laser & Optoelectronics Progress, 2019, 56(15): 151504

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