by

*Anti-Aliasing through the use of Coordinate Transformations*, Ken Turkowski, ACM Transactions on Graphics, July 1982.- The convolution integral is applied to edges and lines, which results in two transformations of radially-symmetric convolution kernels into univariate functions of the Euclidean point-line distance that facilitate anti-aliasing of lines and edges.

*Filters for Common Resampling Tasks*, Ken Turkowski, Graphics Gems I, Academic Press, 1990, pp. 147-165.- Filter coefficients are tabulated for interpolation and integral decimation (by 2, 3, and 4) for various kernels: tent, Gaussian (of two physically meaningful variances), and Lanczos-windowed sinc functions (with half-domain intervals of two and three). Their frequency-domain properties are analyzed and compared for analog and digital implementations. Two new zero-phase, decimate-by-two utility filters with shift-add implementations are proposed and analyzed.

*Anti-Aliasing in Topological Color Spaces*, Ken Turkowski, SIGGRAPH Conference Proceedings 1986.- A topological taxonomy of color spaces is presented. A new family of color spaces, based on a vector number system, is shown to be particularly useful for anti-aliasing between pairs (or triads) out of a chosen set of "primary" colors.

*Scanline-Order Image Warping using Error-Controlled Adaptive Piecewise Polynomial Approximation*, Ken Turkowski, Apple Computer Technical Report, 2002.*The Differential Geometry of Texture Mapping and Shading*, Ken Turkowski, Apple Computer Technical Report, 1992.- Mathematical equations are given for differential surface geometry, ray-tracing and shading, with applications for anti-aliasing of shaders with texture-mapping, bump-mapping and environmental-mapping components.

*The Differential Geometry of Texture Mapping*, Ken Turkowski, Apple Technical Report no. 10, May 1988.- Transformations between neighborhoods of screen space and texture space, including incremental computation and anti-aliasing.

*Circular Arc Subdivision*, Ken Turkowski, Graphics Gems V, Academic Press, 1995, pp. 168-172.- Presentation of a robust method for subdivision of circular arcs with low curvature.

*The Differential Geometry of Parametric Primitives*, Ken Turkowski, Apple Technical Report KT-23, January 26, 1990.- Derivation of the expressions for first and second derivatives, normal, metric tensor and curvature tensor for spheres, cones, cylinders, and tori.

*Computing 2D Polygon Moments Using Green's Theorem*, Ken Turkowski, Apple Technical Report, December 1997.- Expressions are derived for 2D polygon area, centroid, and inertial tensor in terms of polygon vertices.

*Fixed-Point Trigonometry with CORDIC Iterations*, Ken Turkowski, Graphics Gems I, Academic Press, 1990, pp. 494-497.- Algorithm for fixed-point computation of sine, cosine, arctangent, rectangular-to-polar conversion, and polar-to-rectangular conversion. Includes an implementation in
*C*.

- Algorithm for fixed-point computation of sine, cosine, arctangent, rectangular-to-polar conversion, and polar-to-rectangular conversion. Includes an implementation in
*The Use of Coordinate Frames in Computer Graphics*, Ken Turkowski, Graphics Gems I, Academic Press, 1990, pp. 522-532.- Transformations can be specified easily, and without trigonometry, through the use of
*coordinate frames*.

- Transformations can be specified easily, and without trigonometry, through the use of
*Properties of Surface-Normal Transformations*, Ken Turkowski, Graphics Gems I, Academic Press, 1990, pp. 539-547.- It is well-known that surface normals are transformed by the inverse transpose of the linear portion of an affine transformation applied to points. The implications of this are explored, with applications to the optimization of shading computations.

*Image Registration*, Ken Turkowski, Apple Computer Technical Report.- A generalized representation for the error, gradient, and Hessian is derived for least squares image registration. This is further specialized to projective mappings.

*Creating Image-Based VR Using a Self-Calibrating Fisheye Lens*, Yalin Xiong and Ken Turkowski, Computer Vision and Pattern Recognition 1997 Conference, San Juan, Puerto Rico.- A series of fisheye photographs are registered by optimization over the parameters of camera rotations, image centers, image radii, polynomial radial lens distortion, image brightness and contrast. These are then projected to a cube, a cylinder, or a sphere to yield an analytically simple environment map that can be reprojected to an arbitrary plane at interactive rates in an image-based virtual reality system such as QuickTimeVR™.

*Registration, Calibration and Blending in Creating High Quality Panoramas*, Yalin Xiong and Ken Turkowski, Fourth IEEE Workshop on Applications of Computer Vision, Princeton, New Jersey, October 19-21, 1998, pp. 69-74.- This paper presents a system for creating a full 360-degree panorama from rectilinear images captured from a single nodal position. The solution to the problem is divided into three steps. The first step registers all overlapping images projectively, using a combination of a gradient-based optimization method and a correlation-based linear search. The second step propagates the projective pairwise registration globally, while minimizing discreptancies. The third step re-projects all images onto a panorama by a Laplacian-pyramid-based blending.

*Computing the Inverse Square Root*, Ken Turkowski, Graphics Gems V, Academic Press, 1995, pp. 16-21.- A fast, iterative algorithm is presented for computing the inverse square root, a function desirable for renormalization of interpolated surface normals suring Phong shading. Includes an implementation in
*C*.

- A fast, iterative algorithm is presented for computing the inverse square root, a function desirable for renormalization of interpolated surface normals suring Phong shading. Includes an implementation in
*Fixed-Point Square Root*, Ken Turkowski, Graphics Gems V, Academic Press, 1995, pp. 22-24.- A fast, accurate method is presented for the computation of the square root in fixed-point arithmetic. Includes an implementation in
*C*.

- A fast, accurate method is presented for the computation of the square root in fixed-point arithmetic. Includes an implementation in
*Computing the Cube Root*, Ken Turkowski, Apple Technical Report #KT-32, 1998.- Two methods are given to compute the cube root of a number, signifincatly faster than pow(
*x*,1.0/3.0). An implementation in C is included.

- Two methods are given to compute the cube root of a number, signifincatly faster than pow(

[ My QuickTime VR Page | My Résumé | My Home Page ]

[ QuickTime VR Home Page | QuickTime Home Page | Apple Home Page]

last revised: