平移法绘制平铺图形

几何画板及绘图内容加载中，请稍等……

2014-03-30 05:22

多边形向量

所属专题 Tesselation by Translation Tesselation by Translation

本范例演示如何通过平移操作绘制平面图形的平铺效果。涉及的核心数学概念包括平移变换、向量、多边形构造等。作图要点使用了GeoGebra的Polygon、AttachCopyToView、Point、Vector、Translate等命令和对象，通过平移向量生成多个图形副本，实现平铺。适合高中阶段学生学习几何变换和空间图形构造。

GeoGebra 命令及参数

Polygon(A, B, 4) → poly1, a, b, c, d, C, D
AttachCopyToView(PolyLine[(3.66, -3.72), (3.58, -3.74), (3.52, -3.7600000000000002), (3.46, -3.8000000000000003), (3.4, -3.86), (3.36, -3.92), (3.34, -3.98), (3.3200000000000003, -4.04), (3.3200000000000003, -4.12), (3.3200000000000003, -4.2), (3.3200000000000003, -4.3), (3.3200000000000003, -4.38), (3.2600000000000002, -4.4), (3.16, -4.42), (3.1, -4.44), (3.04, -4.46), (2.98, -4.5), (2.92, -4.5200000000000005), (2.86, -4.5600000000000005), (2.8000000000000003, -4.6000000000000005), (2.74, -4.64), (2.72, -4.7), (2.66, -4.74), (2.62, -4.8), (2.56, -4.86), (2.54, -4.94), (2.48, -4.96), (2.4, -4.96), (2.32, -4.96), (2.24, -4.96), (2.18, -4.98), (2.12, -5.0200000000000005), (2.08, -5.08), (2.04, -5.14), (2, -5.2), (2, -5.1000000000000005), (2, -5.0200000000000005), (2, -4.94), (1.94, -4.98), (1.92, -5.04), (1.92, -5.12), (1.9000000000000001, -5.18), (1.8800000000000001, -5.24), (1.8800000000000001, -5.16), (1.8800000000000001, -5.08), (1.8800000000000001, -5), (1.8800000000000001, -4.92), (1.8800000000000001, -4.84), (1.94, -4.76), (2, -4.74), (2.06, -4.7), (2.14, -4.7), (2.22, -4.7), (2.3000000000000003, -4.7), (2.34, -4.64), (2.38, -4.5600000000000005), (2.42, -4.5), (2.48, -4.48), (2.5, -4.4), (2.54, -4.34), (2.6, -4.32), (2.66, -4.26), (2.72, -4.24), (2.62, -4.24), (2.52, -4.24), (2.44, -4.24), (2.38, -4.2), (2.3000000000000003, -4.18), (2.24, -4.16), (2.18, -4.1), (2.14, -4.04), (2.12, -3.98), (2.04, -3.96), (1.98, -3.94), (1.96, -3.88), (1.94, -3.8200000000000003), (1.92, -3.7600000000000002), (1.92, -3.68), (1.9000000000000001, -3.62), (1.9000000000000001, -3.54), (1.9000000000000001, -3.46), (1.92, -3.4), (1.86, -3.38), (1.78, -3.38), (1.7, -3.3200000000000003), (1.68, -3.2600000000000002), (1.6400000000000001, -3.18), (1.62, -3.12), (1.6, -3.06), (1.58, -3), (1.5, -2.96), (1.44, -2.94), (1.3800000000000001, -2.9), (1.36, -2.84), (1.32, -2.7600000000000002), (1.26, -2.68), (1.24, -2.62), (1.2, -2.56), (1.1400000000000001, -2.52), (1.1, -2.58), (1.04, -2.6), (0.96, -2.6), (0.9, -2.62), (0.8200000000000001, -2.58), (0.76, -2.56), (0.68, -2.56), (0.62, -2.6), (0.54, -2.64), (0.48, -2.66), (0.46, -2.72), (0.44, -2.7800000000000002), (0.4, -2.84), (0.36, -2.9), (0.3, -2.94), (0.28, -3), (0.26, -3.06), (0.2, -3.1), (0.2, -3.18), (0.18, -3.2600000000000002), (0.16, -3.3200000000000003), (0.12, -3.38), (0.06, -3.42), (0, -3.44), (-0.06, -3.46), (-0.12, -3.48), (-0.16, -3.54), (-0.18, -3.6), (-0.18, -3.68), (-0.16, -3.74), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke1
Point(a) → E
Point(c) → F
Vector(E, F) → u
Translate(stroke1, v) → stroke1'
Translate(stroke1, u) → stroke1'_1
AttachCopyToView(PolyLine[(-0.1, -3.72), (-0.18, -3.72), (-0.24, -3.74), (-0.3, -3.7800000000000002), (-0.34, -3.84), (-0.36, -3.9), (-0.36, -3.98), (-0.36, -4.0600000000000005), (-0.4, -4), (-0.42, -3.92), (-0.48, -3.96), (-0.48, -4.04), (-0.52, -3.98), (-0.52, -3.9), (-0.52, -3.8200000000000003), (-0.52, -3.74), (-0.48, -3.68), (-0.46, -3.62), (-0.44, -3.56), (-0.44, -3.48), (-0.42, -3.42), (-0.4, -3.36), (-0.38, -3.3000000000000003), (-0.32, -3.2800000000000002), (-0.28, -3.22), (-0.22, -3.18), (-0.2, -3.12), (-0.14, -3.08), (-0.12, -3.02), (-0.06, -2.98), (-0.04, -2.92), (-0.02, -2.84), (0, -2.7800000000000002), (0.04, -2.72), (0.08, -2.66), (0.12, -2.6), (0.14, -2.54), (0.18, -2.48), (0.24, -2.44), (0.3, -2.4), (0.36, -2.36), (0.42, -2.32), (0.44, -2.2600000000000002), (0.5, -2.24), (0.54, -2.18), (0.54, -2.08), (0.58, -2.02), (0.58, -1.94), (0.58, -1.86), (0.56, -1.78), (0.54, -1.72), (0.48, -1.6600000000000001), (0.42, -1.6400000000000001), (0.36, -1.62), (0.3, -1.6), (0.22, -1.6), (0.14, -1.6), (0.06, -1.6), (0, -1.6400000000000001), (-0.04, -1.7), (-0.06, -1.76), (-0.08, -1.82), (-0.1, -1.8800000000000001), (-0.12, -1.94), (-0.16, -2), (-0.18, -2.08), (-0.18, -2.16), (-0.2, -2.22), (-0.22, -2.2800000000000002), (-0.16, -2.2600000000000002), (-0.14, -2.2), (-0.1, -2.12), (-0.08, -2.06), (-0.02, -2), (0.04, -1.96), (0.12, -1.92), (0.18, -1.8800000000000001), (0.24, -1.9000000000000001), (0.24, -1.98), (0.22, -2.04), (0.16, -2.1), (0.12, -2.18), (0.1, -2.24), (0.04, -2.2800000000000002), (-0.04, -2.32), (-0.1, -2.38), (-0.16, -2.42), (-0.2, -2.48), (-0.22, -2.54), (-0.28, -2.56), (-0.36, -2.56), (-0.42, -2.52), (-0.46, -2.46), (-0.48, -2.4), (-0.5, -2.34), (-0.5, -2.2600000000000002), (-0.5, -2.14), (-0.5, -2.06), (-0.5, -1.98), (-0.5, -1.9000000000000001), (-0.48, -1.84), (-0.44, -1.78), (-0.42, -1.7), (-0.38, -1.6400000000000001), (-0.32, -1.56), (-0.3, -1.48), (-0.28, -1.42), (-0.26, -1.36), (-0.24, -1.3), (-0.18, -1.28), (-0.12, -1.26), (-0.06, -1.24), (0, -1.22), (0.08, -1.22), (0.16, -1.22), (0.24, -1.22), (0.32, -1.22), (0.38, -1.26), (0.46, -1.26), (0.54, -1.22), (0.6, -1.18), (0.64, -1.12), (0.66, -1.06), (0.72, -1.02), (0.78, -0.96), (0.84, -0.9400000000000001), (0.9, -0.88), (0.96, -0.84), (1, -0.78), (1.04, -0.72), (1.06, -0.66), (1.08, -0.6), (1.08, -0.52), (1.1, -0.46), (1.1400000000000001, -0.4), (1.16, -0.34), (1.18, -0.28), (1.2, -0.22), (1.22, -0.16), (1.16, -0.12), (1.1400000000000001, -0.06), (1.12, 0), (1.1, 0.08), (1.1, 0.16), (1.1, 0.24), (1.08, 0.3), (1.06, 0.36), (1.04, 0.42), (1.02, 0.48), (1.02, 0.56), (1, 0.62), (1, 0.7000000000000001), (0.9400000000000001, 0.68), (0.88, 0.66), (0.84, 0.6), (0.8200000000000001, 0.54), (0.8, 0.48), (0.76, 0.42), (0.7000000000000001, 0.38), (0.64, 0.36), (0.58, 0.34), (0.52, 0.28), (0.5, 0.22), (0.48, 0.16), (0.46, 0.1), (0.4, 0.06), (0.34, 0.02), (0.28, 0), (0.22, -0.02), (0.14, -0.02), (0.06, -0.02), (-0.02, -0.02), (-0.08, 0), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke2
Point(d) → G
Point(b) → H
Vector(G, H) → w
Translate(stroke2, w) → stroke2'

AI 绘图提示语参考

画一个由四边形构成的平面图形，通过平移操作生成多个副本，形成 tessellation 图案。首先绘制一个四边形，然后找到其两个对角顶点，以这两个点为起点和终点画一个向量。接着，使用这个向量平移四边形，生成第一个副本，再使用四边形的一边向量平移第一个副本，生成第二个副本。最后，将这三个图形组合在一起，形成连续的 tessellation 图案。

以上提示语为根据原始绘图命令整理而来，仅供参考。