![]() dat.gg <- circleLayoutVertices(packing, npoints= 50) # Make the plot ggplot() # Make the bubbles geom_polygon( data = dat.gg, aes(x, y, group = id, fill= as.factor(id)), colour = "black", alpha = 0.6) # Add text in the center of each bubble control its size geom_text( data = data, aes(x, y, size=value, label = group)) scale_size_continuous( range = c( 1, 4)) # General theme: theme_void() theme( legend. I think the Circle packing theorem does not apply as I have a rectangle instead of large circle, different radii An other option is to do an approximation with square packing in rectangle. So if circle one has diameter d1 and circle two has diameter d2 and d1 \ge d2 and the rectangle has sides l and w and l \ge w, then the two circles will fit if d1 \le w and d1 d2 \le l. The rectangle must be as wide as the longer diameter and the longer side as long as the sum of the diameters. Therefore the proportion of the plane covered by the circles is pi/4 0.785398. WolframAlpha can do 2D packing optimization for circles, squares and equilateral triangles, both as the filling objects and as the containers. To pack two circles tightly together is to touch them tangently. The area of the circle is pi and the area of the square is 4 square units. We don't want a linear relationship, since it is the AREA that must be proportionnal to the value # plot(data$radius, data$value) # The next step is to go from one center a radius to the coordinates of a circle that # is drawn by a multitude of straight lines. One important kind of packing problem is to optimize packing plane geometry figures in a bounded 2-dimensional container. # It gives its center (x and y) and its radius, proportional of the value packing <- circleProgressiveLayout(data $value, sizetype= 'area') # We can add these packing information to the initial data frame data <- cbind(data, packing) # Check that radius is proportional to value. ![]() This function return a dataframe with one line per bubble. Essentially, I am trying to pack maximum rectangles into a circle. All the of die will be equal size, either rectangular or square, and the die are all cut from a circular wafer. Cutting Circles and Polygons from Area-Minimizing Rectangles. (The wafer saw cuts only parallel lines) We are, of course, trying to maximize the yield of the die we cut. of the circles in the rectangle height height of the rectangle ( W 1) density ratio of total area occupied by the circles to container area (for an infinite hexagonal packing you get the well-known value Pi/ (2sqrt (3))0. title Pack Circles in the smallest possible Rectangle (CIRCPACK,SEQ401) onText For a given set of circles determine the minimum area rectangle which hosts all circles. # Libraries library(packcircles) library(ggplot2) # Create data data <- ame( group= paste( "Group", letters), value= sample( seq( 1, 100), 20)) # Generate the layout. I work at a nanotech lab where I do silicon wafer dicing.
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