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koch_snowflake_3d.m
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koch_snowflake_3d.m
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% Copyright (c) 2023, Yu Xiong , email:[email protected]
% All rights reserved.
% Civil Aviation University of China (CAUC)
%
% This code is the property of Yu Xiong and is protected under copyright law.
% Redistribution and use of this code, with or without modification, are
% permitted provided that the following conditions are met:
%
% 1. The code is for non-commercial use only.
% 2. Redistributions of the code must retain the above copyright notice,
% this list of conditions, and the following disclaimer.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
% POSSIBILITY OF SUCH DAMAGE.
%
% 版权 © 2023, 熊玉
% 所有权利保留。
% 中国民航大学 (CAUC)
function koch_snowflake_3d(n, h, initial_length)
% 绘制三维科赫雪花,n是迭代次数,h是高度,initial_length是初始边长。
% 初始化顶点
theta = (0:5) * pi/3;
radius = initial_length; % 初始半径,初始边长
vertices = [radius * cos(theta); radius * sin(theta); zeros(1, 6)];
% 准备画图
figure;
hold on;
axis equal;
grid on;
% 中心高度偏移
offset_height = h / 2;
% 计算顶点数组的总长度
num_points_per_side = 4^n - 1; % 每边的顶点数,每次迭代边数增加4倍,减1避免重复计算端点
total_points = 6 * (num_points_per_side + 1); % 总顶点数,+1 为了闭合每边的端点
top_vertices = zeros(3, total_points);
bottom_vertices = zeros(3, total_points);
% 生成顶面和底面顶点数据
current_index = 1;
for i = 1:6
p1 = vertices(:, i);
p2 = vertices(:, mod(i, 6) + 1);
[top_line, bottom_line] = draw_koch_side(p1, p2, n, offset_height, -offset_height);
num_points_in_line = size(top_line, 2);
end_index = current_index + num_points_in_line - 1;
top_vertices(:, current_index:end_index) = top_line;
bottom_vertices(:, current_index:end_index) = bottom_line;
current_index = end_index + 1; % 更新起始索引
end
% 绘制侧面
for i = 1:(total_points-1)
next_index = i + 1;
patch('Vertices', [top_vertices(:, i)'; bottom_vertices(:, i)'; bottom_vertices(:, next_index)'; top_vertices(:, next_index)'], ...
'Faces', [1, 2, 3, 4], ...
'FaceColor', 'cyan', 'EdgeColor', 'b'); % 侧面填充为青色
end
save top top_vertices
% 绘制顶部和底部
fill3(top_vertices(1,:), top_vertices(2,:), top_vertices(3,:), 'r'); % 填充顶部为红色
fill3(bottom_vertices(1,:), bottom_vertices(2,:), bottom_vertices(3,:), 'b'); % 填充底部为蓝色
% 设置视图和坐标轴限制
view(3); % 切换到三维视图
axis([-1.5*radius 1.5*radius -1.5*radius 1.5*radius -offset_height offset_height]);
xlabel('X');
ylabel('Y');
zlabel('Z');
hold off;
end
function [top_line, bottom_line] = draw_koch_side(p1, p2, n, top_offset, bottom_offset)
if n == 0
% 基本情形,绘制直线段
top_line = [p1, p2] + [0;0;top_offset];
bottom_line = [p1, p2] + [0;0;bottom_offset];
else
% 递归分割边缘
dp = (p2 - p1) / 3;
p3 = p1 + dp;
p4 = p1 + 2 * dp;
dp_perp = [0 -1; 1 0; 0 0] * dp(1:2); % 只对x,y分量做旋转
p5 = p1 + 1.5 * dp + dp_perp * sqrt(3) / 2; % Z坐标不变
[top_line1, bottom_line1] = draw_koch_side(p1, p3, n-1, top_offset, bottom_offset);
[top_line2, bottom_line2] = draw_koch_side(p3, p5, n-1, top_offset, bottom_offset);
[top_line3, bottom_line3] = draw_koch_side(p5, p4, n-1, top_offset, bottom_offset);
[top_line4, bottom_line4] = draw_koch_side(p4, p2, n-1, top_offset, bottom_offset);
top_line = [top_line1(:, 1:end-1), top_line2(:, 1:end-1), top_line3(:, 1:end-1), top_line4];
bottom_line = [bottom_line1(:, 1:end-1), bottom_line2(:, 1:end-1), bottom_line3(:, 1:end-1), bottom_line4];
end
end