Add two examples of animation

Author: franko

examples/integral-anim.lua

@@ -0,0 +1,27 @@
+require "graph"
+
+local pi, sin, cos, exp = math.pi, math.sin, math.cos, math.exp
+
+local function integral_fill()
+   local function f(x) return exp(-0.1*x) * cos(x) end
+   local p = graph.plot "y = f(x)"
+   local x0, x1 = 0, 10*pi
+   local cc = graph.fxline(f, x0, x1, k)
+   p.sync = false
+   p:limits(0, -1, 10*pi, 1)
+   p:pushlayer()
+   p:show()
+   local N = 256
+   local yellow = graph.rgba(255,255,0,155)
+   for k= 2, N do
+      local x = x0 + k * (x1-x0) / N
+      local ca = graph.fxline(f, x0, x, k)
+      ca:line_to(x, 0); ca:line_to(0, 0); ca:close()
+      p:clear()
+      p:add(ca, yellow)
+      p:addline(cc)
+      p:flush()
+   end
+end
+
+integral_fill()

examples/vonkoch-anim.lua

@@ -0,0 +1,86 @@
+require "graph"
+
+local pi, sqrt3_2 = math.pi, math.sqrt(3)/2
+
+local sx = {2, 1, -1, -2, -1,  1}
+local sy = {0, 1,  1,  0, -1, -1}
+
+for k=1, 6 do
+    sx[k] = 0.5 * sx[k]
+    sy[k] = sqrt3_2 * sy[k]
+end
+
+local function vonkoch_alpha(n, alpha)
+    local sh = {1, -2, 1}
+    local a, x, y = 0, 0, 0
+    local w = {}
+    for i = 1, n+1 do w[i] = 0 end
+    local s = 1 / (3^n)
+    local line = graph.path(x, y)
+    while w[n+1] == 0 do
+        local x1, y1 = x + (s/3) * sx[a+1], y + (s/3) * sy[a+1]
+        local ap = (a + 1) % 6
+        local x2e, y2e = x1 + (s/3) * sx[ap+1], y1 + (s/3) * sy[ap+1]
+        local x2b, y2b = x + (s/2) * sx[a +1], y + (s/2) * sy[a +1]
+        local x3, y3 = x + (2*s/3) * sx[a+1], y + (2*s/3) * sy[a+1]
+        line:line_to(x1, y1)
+        line:line_to(x2b * (1-alpha) + x2e * alpha, y2b * (1-alpha) + y2e * alpha)
+        line:line_to(x3, y3)
+        x, y = x + s * sx[a+1], y + s * sy[a+1]
+        line:line_to(x, y)
+        for k = 1, n+1 do
+               w[k] = (w[k] + 1) % 4
+               if w[k] ~= 0 then
+                  a = (a + sh[w[k]]) % 6
+                  break
+               end
+        end
+    end
+    return line
+end
+
+-- Create an empty plot (canvas). Since it is created as a "canvas" we
+-- have to explicitily set the limits and perform the flush operation.
+p = graph.canvas("Von Koch's curve")
+p:limits(-0.15, -1, 1.15, 0.3)
+p.units = false
+p:show()
+
+-- Create the inner solid triangle
+local t = graph.path()
+t:move_to(0,0)
+t:line_to(1,0)
+t:line_to(0.5,-sqrt3_2)
+t:close()
+
+-- Defines two colors for the outline and the filling.
+local c = graph.webcolor(1)
+local cfill = graph.rgba(0,0,180,50)
+
+-- Add the inner triangle to the plot and push a new graphical layer.
+-- In this way the triangle will remain whel p:clear() will be called.
+p:add(t, cfill)
+p:pushlayer()
+
+for n = 0, 4 do
+    for alpha = 0, 1.0, 0.01 do
+        p:clear() -- clear the plot
+
+        -- Create the Von Koch's curve segment
+        local v = vonkoch_alpha(n, alpha)
+
+        -- Add the segment three times but rotated and translated with
+        -- a solid fill.
+        p:add(v, cfill)
+        p:add(v, cfill, {}, {{"translate", x=1, y=0}, {"rotate", angle=-2*pi/3}})
+        p:add(v, cfill, {}, {{"translate", x=0.5, y=-sqrt3_2}, {"rotate", angle=-2*2*pi/3}})
+
+        -- Add the same lines that before but only to make the outlines.
+        p:addline(v, c)
+        p:addline(v, c, {}, {{"translate", x=1, y=0}, {"rotate", angle=-2*pi/3}})
+        p:addline(v, c, {}, {{"translate", x=0.5, y=-sqrt3_2}, {"rotate", angle=-2*2*pi/3}})
+
+        -- Flush the plot so that the windows is actually updated on the screeen.
+        p:flush()
+    end
+end