Implement G2 continuity for some nodes

docs/nodes/curve/blend_curves.rst

@@ -66,29 +66,29 @@ This node has the following parameters:
 * **Continuity**. This defines how smooth the connection between initial curves
   and generated blending curves should be. The available options are:
 
-  * **0 - Position**. Blending curve starts at the end of first curve and ends
+  * **C0 - Position**. Blending curve starts at the end of first curve and ends
     at the beginning of the second curve, but no attempts are made to make
     these connections smooth. As a result, the blending curve is always a
     segment of a straight line.
 
     .. image:: https://user-images.githubusercontent.com/14288520/211332041-419c7002-28bb-45ca-b507-238ff4f13dcd.png
       :target: https://user-images.githubusercontent.com/14288520/211332041-419c7002-28bb-45ca-b507-238ff4f13dcd.png
 
-  * **1 - Tangency**. The blending curves are generated so that the tangent
+  * **G1 - Tangency**. The blending curves are generated so that the tangent
     vectors of the curves are equal at their meeting points. The generated
     curves are cubic Bezier curves.
 
     .. image:: https://user-images.githubusercontent.com/14288520/211333493-3dfe0a3f-1143-429f-bd1c-7a9c04ce45bf.png
       :target: https://user-images.githubusercontent.com/14288520/211333493-3dfe0a3f-1143-429f-bd1c-7a9c04ce45bf.png
 
-  * **1b - Bi Arc**. The blending curves are generated as biarc_ curves, i.e.
+  * **G1 - Bi Arc**. The blending curves are generated as biarc_ curves, i.e.
     pairs of circular arcs; they are generated so that the tanent vectors of
     the curves are equal at their meeting points.
 
     .. image:: https://user-images.githubusercontent.com/14288520/211338021-ae8c68d9-bc02-4323-8cc5-8888c0c8ad33.png
       :target: https://user-images.githubusercontent.com/14288520/211338021-ae8c68d9-bc02-4323-8cc5-8888c0c8ad33.png
 
-  * **2 - Normals**. The blending curves are generated so that 1) tangent
+  * **C2 - Smooth Normals**. The blending curves are generated so that 1) tangent
     vectors of the curves are equal at the meeting points; 2) second
     derivatives of the curves are also equal at the meeting points. Thus,
     normal and binormal vectors of the curves are equal at their meeting
@@ -97,7 +97,7 @@ This node has the following parameters:
     .. image:: https://user-images.githubusercontent.com/14288520/211343223-f0c9bc79-bf16-4833-a3cd-6b651d52d099.png
       :target: https://user-images.githubusercontent.com/14288520/211343223-f0c9bc79-bf16-4833-a3cd-6b651d52d099.png
 
-  * **3 - Curvature**. The blending curves are generated so that 1) tangent
+  * **C3 - Smooth Curvature**. The blending curves are generated so that 1) tangent
     vectors of the curves are equal at the meeting points; 2) second and third
     derivatives of the curves are also equal at the meeting points. Thus,
     normal and binormal vectors of the curves, as well as curvatures of the
@@ -107,6 +107,14 @@ This node has the following parameters:
     .. image:: https://user-images.githubusercontent.com/14288520/211344080-1146e033-7296-4f92-9bd5-f36348d7ebd7.png
       :target: https://user-images.githubusercontent.com/14288520/211344080-1146e033-7296-4f92-9bd5-f36348d7ebd7.png
 
+  * **G2 - Curvature**. This means continuous curvature. Curvature comb rim
+    line is continuous, but not smooth. In this sense, this mode is similar to
+    "C2 - Smooth Normals" mode. But with G2 mode, the blending curve does not
+    go so far from touching points as in C2 or C3 mode.
+
+    .. image:: https://user-images.githubusercontent.com/284644/210864882-de4a8a95-f73a-42d3-b30f-1f01ad7a6c33.png
+      :target: https://user-images.githubusercontent.com/284644/210864882-de4a8a95-f73a-42d3-b30f-1f01ad7a6c33.png
+
   The default value is **1 - Tangency**.
 
 * **Blend**. These defines how the curves to be joined are provided. The available options are:
@@ -190,4 +198,4 @@ Cycle one curve
   :target: https://user-images.githubusercontent.com/14288520/211379616-f43aac03-c3a5-4023-8f51-e243990c74e4.png
 
 * Scene-> :doc:`Bezier Input </nodes/exchange/bezier_in>`
-* Viz-> :doc:`Viewer Draw Curve </nodes/viz/viewer_draw_curve>`
+* Viz-> :doc:`Viewer Draw Curve </nodes/viz/viewer_draw_curve>`

docs/nodes/surface/blend_surface.rst

@@ -55,6 +55,21 @@ Parameters
 
 This node has the following parameters:
 
+* **Smoothness**. This defines how smooth the connection between initial
+  surfaces and generated blending surface should be. The available options are:
+
+  * **G1 - Tangency**. Exact matching of tangents is guaranteed.
+
+    .. image:: https://user-images.githubusercontent.com/284644/210866314-f05d511e-8ae9-46aa-88b1-feb030c67ce1.png
+      :target: https://user-images.githubusercontent.com/284644/210866314-f05d511e-8ae9-46aa-88b1-feb030c67ce1.png
+
+  * **G2 - Curvature**. Matching of geometric curvature is guaranteed.
+
+    .. image:: https://user-images.githubusercontent.com/284644/210866466-2a0d5628-0d00-48ad-a28b-5c037d84b7fd.png
+      :target: https://user-images.githubusercontent.com/284644/210866466-2a0d5628-0d00-48ad-a28b-5c037d84b7fd.png
+
+   The default option is **G1 - Tangency**.
+
 * **Curve1**. This defines where the blending surface should touch the first surface. The available options are:
 
   * **Min U**. Use the edge of the surface with the minimum value of U parameter.
@@ -133,4 +148,4 @@ An example of NURBS mode:
 * Surfaces-> :doc:`Plane (Surface) </nodes/surface/plane>`
 * Surfaces-> :doc:`Apply Field to Surface </nodes/surface/apply_field_to_surface>`
 * Matrix-> :doc:`Matrix In </nodes/matrix/matrix_in_mk4>`
-* Viz-> :doc:`Viewer Draw Surface </nodes/viz/viewer_draw_surface>`
+* Viz-> :doc:`Viewer Draw Surface </nodes/viz/viewer_draw_surface>`

nodes/curve/blend_curves.py

@@ -43,8 +43,8 @@ def update_sockets(self, context):
         self.inputs['Curve1'].hide_safe = self.mode != 'TWO'
         self.inputs['Curve2'].hide_safe = self.mode != 'TWO'
         self.inputs['Curves'].hide_safe = self.mode != 'N'
-        self.inputs['Factor1'].hide_safe = self.smooth_mode != '1'
-        self.inputs['Factor2'].hide_safe = self.smooth_mode != '1'
+        self.inputs['Factor1'].hide_safe = self.smooth_mode not in ['1', 'G2']
+        self.inputs['Factor2'].hide_safe = self.smooth_mode not in ['1', 'G2']
         self.inputs['Parameter'].hide_safe = self.smooth_mode != '1b'
         updateNode(self, context)
 
@@ -60,11 +60,12 @@ def update_sockets(self, context):
         update = update_sockets)
 
     smooth_modes = [
-            ('0',  "0 - Position", "Connect ends of curves with straight line segment", 0),
-            ('1',  "1 - Tangency", "Connect curves such that their tangents are smoothly joined", 1),
-            ('1b', "1b - Bi Arc", "Connect curves with Bi Arc, such that tangents are smoothly joined", 2),
-            ('2',  "2 - Normals", "Connect curves such that their normals (second derivatives) are smoothly joined", 3),
-            ('3',  "3 - Curvature", "Connect curves such that their curvatures (third derivatives) are smoothly joined", 4)
+            ('0', "C0 - Position", "Connect ends of curves with straight line segment", 0),
+            ('1', "G1 - Tangency", "Connect curves such that their tangents are continuosly joined", 1),
+            ('1b', "G1 - Bi Arc", "Connect curves with Bi Arc, such that tangents are continuosly joined", 2),
+            ('2', "C2 - Smooth Normals", "Connect curves such that their second derivatives are continuosly joined", 3),
+            ('3', "C3 - Smooth Curvature", "Connect curves such that their third derivatives are continuosly joined", 4),
+            ('G2', "G2 - Curvature", "Connect curves such that their tangents, normals and curvatures are continuosly joined", 5)
         ]
 
     smooth_mode : EnumProperty(
@@ -245,8 +246,23 @@ def process(self):
                                         curve1_end, tangent_1_end, second_1_end, third_1_end,
                                         curve2_begin, tangent_2_begin, second_2_begin, third_2_begin)
                         controls = [p.tolist() for p in new_curve.points]
-                    else:
-                        raise Exception("Unsupported smooth level")
+                    elif smooth == 'G2':
+                        tangent_1_end = curve1.tangent(t_max_1)
+                        tangent_2_begin = curve2.tangent(t_min_2)
+                        tangent1 = factor1 * tangent_1_end
+                        tangent2 = factor2 * tangent_2_begin
+                        normal_1_end = curve1.main_normal(t_max_1)
+                        normal_2_begin = curve2.main_normal(t_min_2)
+                        curvature_1_end = curve1.curvature(t_max_1)
+                        curvature_2_begin = curve2.curvature(t_min_2)
+
+                        #print(f"Bz: P1 {curve1_end}, P2 {curve2_begin}, T1 {tangent1}, T2 {tangent2}, n1 {normal_1_end}, n2 {normal_2_begin}, c1 {curvature_1_end}, c2 {curvature_2_begin}")
+                        new_curve = SvBezierCurve.from_tangents_normals_curvatures(
+                                        curve1_end, curve2_begin,
+                                        tangent1, tangent2,
+                                        normal_1_end, normal_2_begin,
+                                        curvature_1_end, curvature_2_begin)
+                        controls = new_curve.get_control_points().tolist()
 
                     # There is two templates of result:
                     # 1. curve1 new_curve1 curve2 new_curve2 curve3 [new_curve3 curve4]/cyclic->curve1

nodes/curve/fillet_curve.py

@@ -17,6 +17,7 @@
 from sverchok.utils.curve.nurbs import SvNurbsCurve
 from sverchok.utils.curve.fillet import (
         SMOOTH_POSITION, SMOOTH_TANGENT, SMOOTH_ARC, SMOOTH_BIARC, SMOOTH_QUAD, SMOOTH_NORMAL, SMOOTH_CURVATURE,
+        SMOOTH_G2,
         fillet_polyline_from_curve, fillet_nurbs_curve
     )
 from sverchok.utils.handle_blender_data import keep_enum_reference
@@ -69,6 +70,7 @@ def get_smooth_modes(self, context):
             items.append((SMOOTH_BIARC, "1 - Bi Arc", "Connect segments with Bi Arc, such that tangents are smoothly joined", 2))
             #items.append((SMOOTH_NORMAL, "2 - Normals", "Connect segments such that their normals (second derivatives) are smoothly joined", 3))
             #items.append((SMOOTH_CURVATURE, "3 - Curvature", "Connect segments such that their curvatures (third derivatives) are smoothly joined", 4))
+            #items.append((SMOOTH_G2, "G2 - Curvature", "Connect curves such that their tangents, normals and curvatures are continuosly joined", 6))
         else:
             items.append((SMOOTH_ARC, "1 - Circular Arc", "Connect segments with circular arcs", 5))
         return items

nodes/surface/blend_surface.py

@@ -54,6 +54,23 @@ def update_sockets(self, context):
             default = 'UMIN',
             update = update_sockets)
 
+    tangency_modes = [
+            (SvBlendSurface.G1, "G1 - Tangency", "G1 tangency: match tangent vectors", 0),
+            (SvBlendSurface.G2, "G2 - Curvature", "G2 tangency: match tangent vectors, normal vectors and curvature values", 1)
+        ]
+
+    tangency_mode : EnumProperty(
+            name = "Smoothness",
+            description = "How smooth the tangency should be",
+            items = tangency_modes,
+            update = updateNode)
+
+    absolute_bulge : BoolProperty(
+            name = "Absolute bulge",
+            description = "If checked, then bulge values specified are actual required tangent vector lengths; otherwise, bulge values are specified as multipliers of surface's tangent vectors",
+            default = True,
+            update = updateNode)
+
     bulge1 : FloatProperty(
             name = "Bulge1",
             description = "Bulge factor for the first surface; set to negative value to bulge in another direction",
@@ -90,7 +107,19 @@ def update_sockets(self, context):
             min = 3,
             update = updateNode)
 
+    ortho_modes = [
+            ('3D', "3D space", "Make V isolines of the surface orthogonal to touching curves in 3D space", 0),
+            ('UV', "UV space", "Make V isolines of the surface continue isolines in original surfaces UV space", 1)
+        ]
+
+    ortho_mode : EnumProperty(
+            name = "Ortho mode",
+            items = ortho_modes,
+            default = '3D', # default for pre-existing nodes
+            update = updateNode)
+
     def draw_buttons(self, context, layout):
+        layout.prop(self, 'tangency_mode')
         box = layout.row(align=True)
         box.prop(self, 'curve1_mode', text='')
         box.prop(self, 'flip1', toggle=True, text='Flip')
@@ -99,6 +128,11 @@ def draw_buttons(self, context, layout):
         box.prop(self, 'flip2', toggle=True, text='Flip')
         layout.prop(self, 'use_nurbs')
 
+    def draw_buttons_ext(self, context, layout):
+        self.draw_buttons(context, layout)
+        layout.prop(self, 'ortho_mode')
+        #layout.prop(self, 'absolute_bulge')
+
     def sv_init(self, context):
         self.inputs.new('SvSurfaceSocket', 'Surface1')
         self.inputs.new('SvCurveSocket', 'UVCurve1')
@@ -108,6 +142,7 @@ def sv_init(self, context):
         self.inputs.new('SvStringsSocket', 'Bulge2').prop_name = 'bulge2'
         self.inputs.new('SvStringsSocket', 'Samples').prop_name = 'samples'
         self.outputs.new('SvSurfaceSocket', 'Surface')
+        self.ortho_mode = 'UV' # default for new nodes
         self.update_sockets(context)
 
     def make_uv_curve(self, surface, mode, flip):
@@ -159,6 +194,8 @@ def process(self):
         bulge2_s = ensure_nesting_level(bulge2_s, 2)
         samples_s = ensure_nesting_level(samples_s, 2)
 
+        absolute_bulge = (self.tangency_mode == SvBlendSurface.G1)
+
         surfaces_out = []
         for params in zip_long_repeat(surface1_s, uv_curve1_s, bulge1_s, surface2_s, uv_curve2_s, bulge2_s, samples_s):
             new_surfaces = []
@@ -173,9 +210,16 @@ def process(self):
                     curve2 = reverse_curve(curve2)
 
                 if self.use_nurbs:
-                    surface = nurbs_blend_surfaces(surface1, surface2, curve1, curve2, bulge1, bulge2, 3, samples)
+                    surface = nurbs_blend_surfaces(surface1, surface2, curve1, curve2, bulge1, bulge2, 3, samples,
+                                absolute_bulge = absolute_bulge,
+                                tangency = self.tangency_mode,
+                                ortho_mode = self.ortho_mode,
+                                logger = self.sv_logger)
                 else:
-                    surface = SvBlendSurface(surface1, surface2, curve1, curve2, bulge1, bulge2)
+                    surface = SvBlendSurface(surface1, surface2, curve1, curve2, bulge1, bulge2,
+                                absolute_bulge = absolute_bulge,
+                                tangency = self.tangency_mode,
+                                ortho_mode = self.ortho_mode)
                 new_surfaces.append(surface)
             surfaces_out.append(new_surfaces)