In virtual colonoscopy, colon conformal flattening plays an important role, which unfolds the colon wall surface to a rectangle planar image and preserves local shapes by conformal mapping, so that the cancerous polyps and other abnormalities can be easily and thoroughly recognized and visualized without missing hidden areas. In such maps, the anatomical landmarks (taeniae coli, flexures, and haustral folds) are naturally mapped to convoluted curves on 2D domain, which poses difficulty for comparing shapes from geometric feature details. Understanding the nature of landmark curves to the whole surface structure is meaningful but it remains challenging and open. In this work, we present a novel and effective colon flattening method based on quasiconformal mapping, which straightens the main anatomical landmark curves with least conformality (angle) distortion. It provides a canonical and straightforward view of the long, convoluted and folded tubular colon surface. The computation is based on the holomorphic 1-form method with landmark straightening constraints and quasiconformal optimization, and has linear time complexity due to the linearity of 1-forms in each iteration. Experiments on various colon data demonstrate the efficiency and efficacy of our algorithm and its practicability for polyp detection and findings visualization; furthermore, the result reveals the geometric characteristics of anatomical landmarks on colon surfaces.