We present a planarity constraint and a novel three-dimensional (3D) point reconstruction algorithm for a multiview laser range slit scanner. The constraint is based on the fact that all observed points on a projected laser line lie on the same plane of laser light in 3D. The parameters of the plane of laser light linearly parametrize a homography between a pair of images of the laser points. This homography can be recovered from point correspondences derived from epipolar geometry. The use of the planar constraint reduces outliers in the reconstruction and allows for the reconstruction of points seen in only one view. We derive an optimal reconstruction of points subject to the planar constraint and compare the accuracy to the suboptimal approach in prior work. We also construct a catadioptric stereo rig with high quality optical components to remove error due to camera synchronization and non-uniform laser projection. The reconstruction results are compared to prior work that uses inexpensive optics and two cameras.