A method comprising: providing in a scanner including a projector, a first camera, a second camera, and a processing system, the projector, the first camera, and the second camera having given relative positions; projecting from a reference plane of the projector an uncoded pattern of uncoded spots, the uncoded spots having no internal structure that enables it to be distinguished from other uncoded elements that are projected, the uncoded spots being projected onto an object; capturing the uncoded spots on the object with the first camera to obtain a first image; capturing the uncoded spots on the object with the second camera to obtain a second image; with the processing system, determining three-dimensional coordinates of a first point on the object based on the uncoded spots in the reference plane, the uncoded spots in the first image, the uncoded spots in the second image, the given relative positions of the projector, the first camera and the second camera, and based on selecting an intersection set only using spots in the first image, in the second image and in the reference plane, without using epipolar constraints, the intersection set including a first uncoded spot from the reference plane with a second uncoded spot from the first image and a third uncoded spot from the second image, wherein the first spot, the second spot, and the third spot are selected based at least in part on a criterion for a nearness of intersection of a first line, a second line, and a third line, the first line being a line drawn from the selected second spot through a perspective center of the first camera, the second line being a line drawn from the selected third spot through a perspective center of the second camera, the third line being a line drawn from the selected first spot through a perspective center of the projector; and storing the determined 3D coordinates of the first point on the object. providing in a scanner including a projector, a first camera, a second camera, and a processing system, the projector, the first camera, and the second camera having given relative positions; projecting from a reference plane of the projector an uncoded pattern of uncoded spots, the uncoded spots having no internal structure that enables it to be distinguished from other uncoded elements that are projected, the uncoded spots being projected onto an object; capturing the uncoded spots on the object with the first camera to obtain a first image; capturing the uncoded spots on the object with the second camera to obtain a second image; with the processing system, determining three-dimensional coordinates of a first point on the object based on the uncoded spots in the reference plane, the uncoded spots in the first image, the uncoded spots in the second image, the given relative positions of the projector, the first camera and the second camera, and based on selecting an intersection set only using spots in the first image, in the second image and in the reference plane, without using epipolar constraints, the intersection set including a first uncoded spot from the reference plane with a second uncoded spot from the first image and a third uncoded spot from the second image, wherein the first spot, the second spot, and the third spot are selected based at least in part on a criterion for a nearness of intersection of a first line, a second line, and a third line, the first line being a line drawn from the selected second spot through a perspective center of the first camera, the second line being a line drawn from the selected third spot through a perspective center of the second camera, the third line being a line drawn from the selected first spot through a perspective center of the projector; and storing the determined 3D coordinates of the first point on the object.