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I am trying to create a new node type (NOT a node group). For example a node that takes two floats as inputs and returns another float as output, and I can do whatever with python in between.

I saw "Custom Nodes" (custom_nodes.py) in Blender's scripting templates but it doesn't seem to do anything when run. I was expecting to see a new menu in Shader Editor when I press shift+a. I'm not even sure if this the right template.

Every example I have found so far was about adding nodes to materials. So I may not be using correct keywords.

Here is the standard custom_nodes.py template in Blender:

import bpy
from bpy.types import NodeTree, Node, NodeSocket

# Implementation of custom nodes from Python


# Derived from the NodeTree base type, similar to Menu, Operator, Panel, etc.
class MyCustomTree(NodeTree):
    # Description string
    '''A custom node tree type that will show up in the editor type list'''
    # Optional identifier string. If not explicitly defined, the python class name is used.
    bl_idname = 'CustomTreeType'
    # Label for nice name display
    bl_label = "Custom Node Tree"
    # Icon identifier
    bl_icon = 'NODETREE'


# Custom socket type
class MyCustomSocket(NodeSocket):
    # Description string
    '''Custom node socket type'''
    # Optional identifier string. If not explicitly defined, the python class name is used.
    bl_idname = 'CustomSocketType'
    # Label for nice name display
    bl_label = "Custom Node Socket"

    # Enum items list
    my_items = (
        ('DOWN', "Down", "Where your feet are"),
        ('UP', "Up", "Where your head should be"),
        ('LEFT', "Left", "Not right"),
        ('RIGHT', "Right", "Not left"),
    )

    my_enum_prop: bpy.props.EnumProperty(
        name="Direction",
        description="Just an example",
        items=my_items,
        default='UP',
    )

    # Optional function for drawing the socket input value
    def draw(self, context, layout, node, text):
        if self.is_output or self.is_linked:
            layout.label(text=text)
        else:
            layout.prop(self, "my_enum_prop", text=text)

    # Socket color
    def draw_color(self, context, node):
        return (1.0, 0.4, 0.216, 0.5)


# Mix-in class for all custom nodes in this tree type.
# Defines a poll function to enable instantiation.
class MyCustomTreeNode:
    @classmethod
    def poll(cls, ntree):
        return ntree.bl_idname == 'CustomTreeType'


# Derived from the Node base type.
class MyCustomNode(Node, MyCustomTreeNode):
    # === Basics ===
    # Description string
    '''A custom node'''
    # Optional identifier string. If not explicitly defined, the python class name is used.
    bl_idname = 'CustomNodeType'
    # Label for nice name display
    bl_label = "Custom Node"
    # Icon identifier
    bl_icon = 'SOUND'

    # === Custom Properties ===
    # These work just like custom properties in ID data blocks
    # Extensive information can be found under
    # http://wiki.blender.org/index.php/Doc:2.6/Manual/Extensions/Python/Properties
    my_string_prop: bpy.props.StringProperty()
    my_float_prop: bpy.props.FloatProperty(default=3.1415926)

    # === Optional Functions ===
    # Initialization function, called when a new node is created.
    # This is the most common place to create the sockets for a node, as shown below.
    # NOTE: this is not the same as the standard __init__ function in Python, which is
    #       a purely internal Python method and unknown to the node system!
    def init(self, context):
        self.inputs.new('CustomSocketType', "Hello")
        self.inputs.new('NodeSocketFloat', "World")
        self.inputs.new('NodeSocketVector', "!")

        self.outputs.new('NodeSocketColor', "How")
        self.outputs.new('NodeSocketColor', "are")
        self.outputs.new('NodeSocketFloat', "you")

    # Copy function to initialize a copied node from an existing one.
    def copy(self, node):
        print("Copying from node ", node)

    # Free function to clean up on removal.
    def free(self):
        print("Removing node ", self, ", Goodbye!")

    # Additional buttons displayed on the node.
    def draw_buttons(self, context, layout):
        layout.label(text="Node settings")
        layout.prop(self, "my_float_prop")

    # Detail buttons in the sidebar.
    # If this function is not defined, the draw_buttons function is used instead
    def draw_buttons_ext(self, context, layout):
        layout.prop(self, "my_float_prop")
        # my_string_prop button will only be visible in the sidebar
        layout.prop(self, "my_string_prop")

    # Optional: custom label
    # Explicit user label overrides this, but here we can define a label dynamically
    def draw_label(self):
        return "I am a custom node"


### Node Categories ###
# Node categories are a python system for automatically
# extending the Add menu, toolbar panels and search operator.
# For more examples see release/scripts/startup/nodeitems_builtins.py

import nodeitems_utils
from nodeitems_utils import NodeCategory, NodeItem

# our own base class with an appropriate poll function,
# so the categories only show up in our own tree type


class MyNodeCategory(NodeCategory):
    @classmethod
    def poll(cls, context):
        return context.space_data.tree_type == 'CustomTreeType'


# all categories in a list
node_categories = [
    # identifier, label, items list
    MyNodeCategory('SOMENODES', "Some Nodes", items=[
        # our basic node
        NodeItem("CustomNodeType"),
    ]),
    MyNodeCategory('OTHERNODES', "Other Nodes", items=[
        # the node item can have additional settings,
        # which are applied to new nodes
        # NB: settings values are stored as string expressions,
        # for this reason they should be converted to strings using repr()
        NodeItem("CustomNodeType", label="Node A", settings={
            "my_string_prop": repr("Lorem ipsum dolor sit amet"),
            "my_float_prop": repr(1.0),
        }),
        NodeItem("CustomNodeType", label="Node B", settings={
            "my_string_prop": repr("consectetur adipisicing elit"),
            "my_float_prop": repr(2.0),
        }),
    ]),
]

classes = (
    MyCustomTree,
    MyCustomSocket,
    MyCustomNode,
)


def register():
    from bpy.utils import register_class
    for cls in classes:
        register_class(cls)

    nodeitems_utils.register_node_categories('CUSTOM_NODES', node_categories)


def unregister():
    nodeitems_utils.unregister_node_categories('CUSTOM_NODES')

    from bpy.utils import unregister_class
    for cls in reversed(classes):
        unregister_class(cls)


if __name__ == "__main__":
    register()
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