They carve it that way from a block of wood. That is a lot stronger than attempting to join the curved piece on.

I make canes, walking sticks and hiking staffs,I got steam heat! Steam softens the natural glue between wood fibers and the fibers themselves and allows the wood to be bent, then it's clamped in a jig with the proper bend until it is cool and dry and the bend stays. Usually the blank is over bent as it has a tendency to spring back some. It makes a strong curve since the fibers are not broken and run the full length of the curve.( This is the way bent back chairs and other such stuff is made too.) Sometimes saplings are bent and tied, sometimes over a form or pattern, and then allowed to grow until big enough for a stick or staff. Those bends are the strongest since it is the way the wood 'wants' to be. The fibers have grown and 'glued' thenselves into a curve. They are also expensive, not all the saplings grow the way I want them or even grow up at all. Rarely is the curve cut or carved from a larger piece. That cuts the wood fibers or grain making weak points in the curve, especially when the fibers are short and run across the curve, which is usually right where the stress is greatest. Wanta see somebody move fast? Watch um grap a steaming hot piece of wood and try to force and clamp it into a jig.

You steam it and slowly bend it around a form.

When you just make a couple of sticks, like a family set, then you also can use lamination. The wood is easier to get and you can use different colours like seen in bow making. there is also the possibility to use exotic wood layers. To bend laminations you use also a steambox. Steam and bend the slats, let dry, glue assemple them together, and shape to taste. To prevent the slats from creeping drill holes and glue brass pins in the crutch. This ads detail and prevent the laminations from deforming under pressure.

For severely hard wood- steaming and boiling the tip has worked for me. If its a really twisty wood- I cheat. I pre-drill micro holes with a Dremel to avoid overtensioning. This was before I realized thos Chinese campaign chairs were no bent. Thet're seamed.