{"id":3568,"date":"2025-12-18T14:24:25","date_gmt":"2025-12-18T19:24:25","guid":{"rendered":"https:\/\/blogs.mathworks.com\/graphics-and-apps\/?p=3568"},"modified":"2026-01-30T20:43:27","modified_gmt":"2026-01-31T01:43:27","slug":"gift-bow","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/graphics-and-apps\/2025\/12\/18\/gift-bow\/","title":{"rendered":"A Bow made of Ribbon"},"content":{"rendered":" \r\n\r\n\r\n\r\n
\"Portrait<\/td>\r\nGuest Writer: Eric Ludlam<\/a>\r\n<\/strong>Eric Ludlam is the development manager of MATLAB\u2019s Charting team. Eric has a whopping 27 years of experience working in MATLAB Graphics, starting in MATLAB 5.0! Eric is renowned within MathWorks for his love of trebuchets, catapults and\u00a0Punkin Chunkin. His exceptional graphics demos have appeared in MathWorks\u2019 Community blog, MATLAB blog, and in MATLAB social media feeds.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\n
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Tis the season for a MATLAB holiday algorithm!<\/div>\r\n
The bow we'll make is constructed of several loops of ribbon that emanate out from the origin. We'll use a Fibonacci spiral<\/a> to determine how far each ribbon loop will extend. Then we will compute the path of the ribbon loops in spherical coordinates. We'll use sph2cart<\/span> to convert our theta & phi values of the ribbon paths into Cartesian locations on a sphere.<\/div>\r\n
Once we've computed the geometry for the path of the ribbon, we use streamribbon<\/span><\/a> to create the geometry for the ribbon.<\/div>\r\n
The streamribbon function is often used to compute a ribbon visualization through a volume, but you can pass in your own paths as well. Since each ribbon might be a different length, streamribbon accepts paths as a cell array of vertex arrays (Nx3)<\/span>. Our ribbon is relatively simple, so once we have the geometry of the ribbons, it is easy enough to customize the returned surface objects for the holidays!<\/div>\r\n
If you open a version of this script in MATLAB Online using the link below, all the parameters at the beginning of the script can be manipulated with sliders and a color picker, making it easy for you to design a bow for your own gift.<\/div>\r\n
\"\"<\/div>\r\n\"Open<\/a>\r\n
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nloops = 21; % Number of loops in the bow<\/span><\/div>\r\n<\/div>\r\n
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lwphi = 0.2; % Loop width across phi normalized radians<\/span><\/div>\r\n<\/div>\r\n
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height = 1; % Height of the bow<\/span><\/div>\r\n<\/div>\r\n
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ribbonwidth = 0.3; % Width of ribbon<\/span><\/div>\r\n<\/div>\r\n
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color = 'red'<\/span>; % Color of the ribbon<\/span><\/div>\r\n<\/div>\r\n
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npts = 21; % Number of vertices in a loop (should be odd)<\/span><\/div>\r\n<\/div>\r\n
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% Create geometry for each loop as a line in spherical coordinates<\/span><\/div>\r\n<\/div>\r\n
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% and then convert to cartesian.<\/span><\/div>\r\n<\/div>\r\n
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theta=repmat((1+sqrt(5))*(1:nloops),npts,1)*pi;<\/div>\r\n<\/div>\r\n
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phi=(linspace(.5,1,nloops).^.8+linspace(-lwphi,lwphi,npts)'.*linspace(.8,1,nloops))*pi;<\/div>\r\n<\/div>\r\n
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R=ones(1,nloops).*(1-abs(linspace(-1,1,npts)'.^2));<\/div>\r\n<\/div>\r\n
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[X,Y,Z] = sph2cart(theta,phi,R);<\/div>\r\n<\/div>\r\n
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% Use streamribbon to create the bow's ribbon.<\/span><\/div>\r\n<\/div>\r\n
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% streamribbon needs the columns of our vertices, and of the twist<\/span><\/div>\r\n<\/div>\r\n
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% angle to be provided as a cell array of matrices.<\/span><\/div>\r\n<\/div>\r\n
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streamverts = mat2cell([ reshape(X,[],1) reshape(Y,[],1) reshape(Z,[],1)*height ],repelem(npts,nloops))';<\/div>\r\n<\/div>\r\n
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twistangle = mat2cell(repmat([pi\/2;zeros(npts-1,1)],nloops,1), repelem(npts,nloops))';<\/div>\r\n<\/div>\r\n
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% Display our fancy gift bow<\/span><\/div>\r\n<\/div>\r\n
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clf<\/div>\r\n<\/div>\r\n
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srf=streamribbon(streamverts,twistangle,ribbonwidth);<\/div>\r\n<\/div>\r\n
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view([0 60]);<\/div>\r\n<\/div>\r\n
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set(srf,'FaceColor'<\/span>,color,'EdgeColor'<\/span>,'none<\/span>','FaceLighting'<\/span>,'gouraud'<\/span>);<\/div>\r\n<\/div>\r\n
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axis off tight equal<\/span><\/div>\r\n<\/div>\r\n
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camlight<\/div>\r\n<\/div>\r\n<\/div>\r\n\"\"\r\n\r\n<\/div>\r\n