collada_scene/animate: implement bezier interpolation

_math.lua

@@ -552,6 +552,61 @@ mat4 = {
 
 setmetatable(mat4, mat4)
 
+vec2 = {
+   __call = function(_t, x, y, z)
+      -- newByteData is zero-initialized
+      local data = love.data.newByteData(2 * 4)
+      local f = ffi.cast('float*', data:getFFIPointer())
+      local value = {
+         data = data,
+         f = f,
+      }
+      f[0] = x
+      f[1] = y
+      setmetatable(value, vec2)
+      return value
+   end,
+
+   load_table = function(t)
+      assert(#t == 2)
+      assert(t[1] ~= nil)
+      assert(t[2] ~= nil)
+      return vec2(t[1], t[2])
+   end,
+
+   set_x = function(v, value)
+      return vec2(value, v.f[1])
+   end,
+
+   set_y = function(v, value)
+      return vec2(v.f[0], value)
+   end,
+
+   get_x = function(v)
+      return v.f[0]
+   end,
+
+   get_y = function(v)
+      return v.f[1]
+   end,
+
+   __mul = function(v, s)
+      return vec2(v.f[0] * s,
+                  v.f[1] * s)
+   end,
+
+   __add = function(v1, v2)
+      return vec2(v1.f[0] + v2.f[0],
+                  v1.f[1] + v2.f[1])
+   end,
+
+   print = function(v)
+      print(tostring(v.f[0]) .. " " .. tostring(v.f[1]))
+   end,
+}
+
+setmetatable(vec2, vec2)
+
 vec3 = {
    __call = function(_t, x, y, z)
       -- newByteData is zero-initialized
@@ -561,9 +616,9 @@ vec3 = {
          data = data,
          f = f,
       }
-      f[0] = x or 0
+      f[0] = x
-      f[1] = y or 0
+      f[1] = y
-      f[2] = z or 0
+      f[2] = z
       setmetatable(value, vec3)
       return value
    end,
@@ -732,10 +787,10 @@ vec4 = {
          data = data,
          f = f,
       }
-      f[0] = x or 0
+      f[0] = x
-      f[1] = y or 0
+      f[1] = y
-      f[2] = z or 0
+      f[2] = z
-      f[3] = w or 0
+      f[3] = w
       setmetatable(value, vec4)
       return value
    end,

collada_scene/animate.lua

@@ -35,6 +35,82 @@ local linear_interpolate_value = function(source, frame_ix, parameter_ix, iv)
    return prev + iv * (next - prev)
 end
 
+
+local pow3 = function(f)
+   return f * f * f
+end
+
+local pow2 = function(f)
+   return f * f
+end
+
+local bezier = function(p0, c0, c1, p1, s)
+   return
+        (p0 * pow3(1 - s))
+      + (c0 * 3 * s * pow2(1 - s))
+      + (c1 * 3 * pow2(s) * (1 - s))
+      + (p1 * pow3(s))
+end
+
+local bezier_binary_search = function(p0, c0, c1, p1, want)
+   local low = 0.0
+   local high = 1.0
+
+   local iterations = 0
+   while iterations < 20 do
+      iterations = iterations + 1
+
+      local s = (high + low) * 0.5
+      local bs = bezier(p0, c0, c1, p1, s)
+      local t = vec2.get_x(bs)
+
+      local epsilon = 0.001
+      if (math.abs(t - want) < epsilon) then
+         return vec2.get_y(bs)
+      end
+
+      if t > want then
+        high = s
+      else
+        low = s
+      end
+   end
+
+   print(vec2.get_x(p0), vec2.get_y(p0))
+   print(vec2.get_x(c0), vec2.get_y(c0))
+   print(vec2.get_x(c1), vec2.get_y(c1))
+   print(vec2.get_x(p1), vec2.get_y(p1))
+   assert(false)
+end
+
+local tangent_index = function(source, frame_ix, parameter_ix)
+   local ix = frame_ix * source.stride + parameter_ix * 2
+   x = source.float_array[ix + 0 + 1]
+   y = source.float_array[ix + 1 + 1]
+   return {x, y}
+end
+
+local bezier_sampler = function(sampler, frame_ix, parameter_ix, t)
+   -- P0 is (INPUT[i] , OUTPUT[i])
+   -- C0 (or T0) is (OUT_TANGENT[i][0] , OUT_TANGENT[i][1])
+   -- C1 (or T1) is (IN_TANGENT[i+1][0], IN_TANGENT[i+1][1])
+   -- P1 is (INPUT[i+1], OUTPUT[i+1])
+
+   local frame0_input = sampler.input.float_array[frame_ix + 0 + 1]
+   local frame1_input = sampler.input.float_array[frame_ix + 1 + 1]
+
+   local frame0_output = sampler.output.float_array[(frame_ix + 0) * sampler.output.stride + parameter_ix + 1]
+   local frame1_output = sampler.output.float_array[(frame_ix + 1) * sampler.output.stride + parameter_ix + 1]
+
+   local p0 = vec2(frame0_input, frame0_output)
+   local c0 = vec2.load_table(tangent_index(sampler.out_tangent, frame_ix + 0, parameter_ix))
+   local c1 = vec2.load_table(tangent_index(sampler.in_tangent, frame_ix + 1, parameter_ix))
+   local p1 = vec2(frame1_input, frame1_output)
+
+   return bezier_binary_search(p0, c0, c1, p1, t)
+end
+
+
 local apply_transform_target = function(transform, channel_target_attribute, value)
    if transform.type == collada_types.transform_type.TRANSLATE or transform.type == collada_types.transform_type.SCALE then
       if channel_target_attribute == collada_types.target_attribute.X then
@@ -81,7 +157,8 @@ local animate_channel_segment = function(channel, transform, frame_ix, t)
    for parameter_ix = 0, target_attributes_count-1 do
       local interpolation = channel.source_sampler.interpolation.interpolation_array[frame_ix]
       local value
-      if false then
+      if interpolation == collada_types.interpolation.BEZIER then
+         value = bezier_sampler(channel.source_sampler, frame_ix, parameter_ix, t)
       else
          local iv = linear_interpolate_iv(channel.source_sampler.input, frame_ix, t)
          value = linear_interpolate_value(channel.source_sampler.output, frame_ix, parameter_ix, iv)

scene/test/test.lua

@@ -30,18 +30,18 @@ local array_node_torus_knot23_translation_x_output_array = {
   -21.94384,
 }
 local array_node_torus_knot23_translation_x_intangent_array = {
-  {-0.3329306, -21.94384},
+  -0.3329306, -21.94384,
-  {0.667, 7.158293},
+  0.667, 7.158293,
-  {1.667, 40.64392},
+  1.667, 40.64392,
-  {2.667, 15.03987},
+  2.667, 15.03987,
-  {3.222333, -21.94384},
+  3.222333, -21.94384,
 }
 local array_node_torus_knot23_translation_x_outtangent_array = {
-  {0.333, -21.94384},
+  0.333, -21.94384,
-  {1.333, 28.00002},
+  1.333, 28.00002,
-  {2.333, 40.64392},
+  2.333, 40.64392,
-  {3.111, -5.801854},
+  3.111, -5.801854,
-  {3.666264, -21.94384},
+  3.666264, -21.94384,
 }
 local array_node_torus_knot23_translation_x_interpolation_array = {
   collada_types.interpolation.BEZIER,
@@ -97,18 +97,18 @@ local array_node_torus_knot23_translation_y_output_array = {
   -1.68812e-14,
 }
 local array_node_torus_knot23_translation_y_intangent_array = {
-  {-0.3329306, -1.68812e-14},
+  -0.3329306, -1.68812e-14,
-  {0.667, 24.27013},
+  0.667, 24.27013,
-  {1.667, -12.4935},
+  1.667, -12.4935,
-  {2.667, 9.835234},
+  2.667, 9.835234,
-  {3.222333, -1.68812e-14},
+  3.222333, -1.68812e-14,
 }
 local array_node_torus_knot23_translation_y_outtangent_array = {
-  {0.333, -1.68812e-14},
+  0.333, -1.68812e-14,
-  {1.333, 24.27013},
+  1.333, 24.27013,
-  {2.333, -12.4935},
+  2.333, -12.4935,
-  {3.111, 9.835234},
+  3.111, 9.835234,
-  {3.666264, -1.68812e-14},
+  3.666264, -1.68812e-14,
 }
 local array_node_torus_knot23_translation_y_interpolation_array = {
   collada_types.interpolation.BEZIER,
@@ -164,18 +164,18 @@ local array_node_torus_knot23_translation_z_output_array = {
   45.45129,
 }
 local array_node_torus_knot23_translation_z_intangent_array = {
-  {-0.3329306, 45.45129},
+  -0.3329306, 45.45129,
-  {0.667, 45.45129},
+  0.667, 45.45129,
-  {1.667, 45.45129},
+  1.667, 45.45129,
-  {2.667, 45.45129},
+  2.667, 45.45129,
-  {3.222333, 45.45129},
+  3.222333, 45.45129,
 }
 local array_node_torus_knot23_translation_z_outtangent_array = {
-  {0.333, 45.45129},
+  0.333, 45.45129,
-  {1.333, 45.45129},
+  1.333, 45.45129,
-  {2.333, 45.45129},
+  2.333, 45.45129,
-  {3.111, 45.45129},
+  3.111, 45.45129,
-  {3.666264, 45.45129},
+  3.666264, 45.45129,
 }
 local array_node_torus_knot23_translation_z_interpolation_array = {
   collada_types.interpolation.BEZIER,
@@ -235,22 +235,22 @@ local array_node_torusknot25_rotationz_angle_output_array = {
   -2.386905,
 }
 local array_node_torusknot25_rotationz_angle_intangent_array = {
-  {-0.3329306, -2.386905},
+  -0.3329306, -2.386905,
-  {0.3335, -38.2941},
+  0.3335, -38.2941,
-  {0.8335, -59.67817},
+  0.8335, -59.67817,
-  {1.3335, -40.14935},
+  1.3335, -40.14935,
-  {1.8335, -99.69791},
+  1.8335, -99.69791,
-  {2.3335, -163.7238},
+  2.3335, -163.7238,
-  {3.055833, -2.386905},
+  3.055833, -2.386905,
 }
 local array_node_torusknot25_rotationz_angle_outtangent_array = {
-  {0.1665, -2.386905},
+  0.1665, -2.386905,
-  {0.6665, -57.37209},
+  0.6665, -57.37209,
-  {1.1665, -59.67817},
+  1.1665, -59.67817,
-  {1.6665, -40.14935},
+  1.6665, -40.14935,
-  {2.1665, -140.8482},
+  2.1665, -140.8482,
-  {2.7775, -163.7238},
+  2.7775, -163.7238,
-  {3.666264, -2.386905},
+  3.666264, -2.386905,
 }
 local array_node_torusknot25_rotationz_angle_interpolation_array = {
   collada_types.interpolation.BEZIER,
@@ -312,22 +312,22 @@ local array_node_torusknot25_rotationy_angle_output_array = {
   -49.62293,
 }
 local array_node_torusknot25_rotationy_angle_intangent_array = {
-  {-0.3329306, -49.62293},
+  -0.3329306, -49.62293,
-  {0.3335, -29.32237},
+  0.3335, -29.32237,
-  {0.8335, 34.11597},
+  0.8335, 34.11597,
-  {1.3335, -56.85069},
+  1.3335, -56.85069,
-  {1.8335, -56.85069},
+  1.8335, -56.85069,
-  {2.3335, -170.1778},
+  2.3335, -170.1778,
-  {3.055833, -49.62293},
+  3.055833, -49.62293,
 }
 local array_node_torusknot25_rotationy_angle_outtangent_array = {
-  {0.1665, -49.62293},
+  0.1665, -49.62293,
-  {0.6665, -1.437308},
+  0.6665, -1.437308,
-  {1.1665, 34.11597},
+  1.1665, 34.11597,
-  {1.6665, -56.85069},
+  1.6665, -56.85069,
-  {2.1665, -56.85069},
+  2.1665, -56.85069,
-  {2.7775, -170.1778},
+  2.7775, -170.1778,
-  {3.666264, -49.62293},
+  3.666264, -49.62293,
 }
 local array_node_torusknot25_rotationy_angle_interpolation_array = {
   collada_types.interpolation.BEZIER,
@@ -389,22 +389,22 @@ local array_node_torusknot25_rotationx_angle_output_array = {
   183.132,
 }
 local array_node_torusknot25_rotationx_angle_intangent_array = {
-  {-0.3329306, 183.132},
+  -0.3329306, 183.132,
-  {0.3335, 256.4932},
+  0.3335, 256.4932,
-  {0.8335, 216.862},
+  0.8335, 216.862,
-  {1.3335, 133.4248},
+  1.3335, 133.4248,
-  {1.8335, 133.4248},
+  1.8335, 133.4248,
-  {2.3335, 146.1407},
+  2.3335, 146.1407,
-  {3.055833, 183.132},
+  3.055833, 183.132,
 }
 local array_node_torusknot25_rotationx_angle_outtangent_array = {
-  {0.1665, 183.132},
+  0.1665, 183.132,
-  {0.6665, 256.4932},
+  0.6665, 256.4932,
-  {1.1665, 175.8802},
+  1.1665, 175.8802,
-  {1.6665, 133.4248},
+  1.6665, 133.4248,
-  {2.1665, 133.4248},
+  2.1665, 133.4248,
-  {2.7775, 162.6932},
+  2.7775, 162.6932,
-  {3.666264, 183.132},
+  3.666264, 183.132,
 }
 local array_node_torusknot25_rotationx_angle_interpolation_array = {
   collada_types.interpolation.BEZIER,
@@ -825,9 +825,9 @@ local instance_controllers_node_torus_knot23 = {
 local instance_lights_node_torus_knot23 = {
 }
 local node_channels_node_torus_knot23 = {
-  node_channel_node_torus_knot23_translation_y,
-  node_channel_node_torus_knot23_translation_x,
   node_channel_node_torus_knot23_translation_z,
+  node_channel_node_torus_knot23_translation_x,
+  node_channel_node_torus_knot23_translation_y,
 }
 local node_node_torus_knot23 = {
   parent_index = -1,
@@ -903,9 +903,9 @@ local instance_controllers_node_torusknot25 = {
 local instance_lights_node_torusknot25 = {
 }
 local node_channels_node_torusknot25 = {
+  node_channel_node_torusknot25_rotationy_angle,
   node_channel_node_torusknot25_rotationz_angle,
   node_channel_node_torusknot25_rotationx_angle,
-  node_channel_node_torusknot25_rotationy_angle,
 }
 local node_node_torusknot25 = {
   parent_index = -1,