In this algorithm, the nearest vertex from the origin in the profile scan lines offset is taken as the start point. The end point is 2d of   dis-

tance away from the start point by clockwise; the scanning    direction

Eq. (5) enables the coordinate of the endpoint Q2(x2, y2) to be calculated.

Fig. 9. Flow chart of the modified scan line algorithm for nozzle path planning.

Fig. 10. Judgment of the inner and outer profiles.

Fig. 11. Intersection calculation of adjacent segments of a polygon after offset.

Fig. 12. The start point and the endpoint of scanning of the profile.

J. Xu et al. / Automation in Construction 76 (2017)  85–96 91

4.2.2. Scanning of the fill

Scanning of the fill refers to filling the rest region of the profile scan. The algorithm is required for scanning the X-axis and Y-axis orientation for the odd and the even layers. An example of scanning the odd layers is provided.

Assuming the maximum coordinate value of the offset profile path

Table 1

Materials prepared for the experiment. Element Description

Sand Natural river sand with 2.1 fineness modulus and 0.12% moisture

content

Cement P.C32.5R Composite  Portland cement

in Y direction isymax, and ymin for the minimum coordinate value, the scanning orientation of the odd scan lines is X-axis positive direction

Water

reducer

Polycarboxylate Superplasticizer

Fiber 3 mm micro polypropylene fibers

and X-axis negative direction for the even ones. This is, however, depen-         

dent on their Y coordinate values. When the scanning distance is D, the number of filling scan lines is n =( ymax −ymin)/D −1, then the equation for the No.i filling scan line is:

Y ¼ ymin  þ iD;   i ¼ 1; 2; 3; …; n: ð6Þ

The scan finishes when the Y coordinate value of a filling scan line meets Y N ymax −D.

When a filling scan line, y = h, intersects with a segment of a offset profile scan line, the equation of the line, where the segment is located, is capably calculated, or rather given, which is here assumed to be Ax+By +C =0 and is expressed as:

. Ax þ By þ C ¼ 0

shapes or even heteromorphosis and no drawings exist; an examples is presented in Fig. 13.

Within the campus at the Huazhong University of Science and Tech- nology (HUST), there are also damaged stone historical plinths similar to those in Fig. 13 and one of them with simple curved surface has been selected for this research to demonstrate the feasibility of the pro- posed digital reproduction process. Notably, the damaged plinth func- tions as an ornamental component for a timber column structure. The role of the plinth is to protect the timber column from water damage and collision, as well provide lateral support and decorative  aesthetics.

According to previous Jump table test, a fine aggregate fiber cement

y ¼ h

ð7Þ

mortar is made up for reproduction of the plinth, which has a 0.3 water– cement ratio and a 1:1 sand: cement ratio, plus 0.1% micro polypropyl-

The intersections of the filling scan line and the segment can be cal- culated using Eq. (7). Assuming the horizontal coordinate of the inter- section is x0, the horizontal coordinate of the odd number of endpoint

corresponding to the intersection is x0 +D, or x0  − D for the even num-