In many applications, the assessment of the internal structures of tubular structures (such as in medical imaging, blood vessels, bronchi, and colon) has become a topic of high interest. Many 3D visualization techniques, such as “fly-through” and curved planar reformation (CPR), have been used for visualization of the lumens for medical applications. However, all the existing visualization techniques generate highly distorted images of real objects. This invention provides direct manipulation based on the centerline of the object and visualization of the 3D internal structures of a tubular object without any noticeable distortion. For the first time ever, the lumens of a human colon is visualized as it is in reality. In many medical applications, this can be used for diagnosis, planning of surgery or stent placements, etc. and consequently improves the quality of healthcare significantly. The same technique can be used in many other applications.