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wire frame modeling:

In the construction of the wire-frame model,the edges of the objects are shown as lines.the image(model) assumes the appearances of a frame constructed out of wire.so, it is called as "wire frame" model.and it is mostly useful in sheet-metal process to know which is driving surface and which is follower surface shown in different colored lines.

solid modeling:

its an improvement over wire-frame models.user can understand how the model is going to be in realism.here the model is displayed in solid objects to the user.even we can use color to the entire model or surface according to our need.

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Q: What is difference between Wireframe model and solid model?
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