A goal of redirected walking (RDW) is to allow large virtual worlds to be explored within small tracking areas. Generalized steering algorithms, such as steer-to-center, simply move the user toward locations that are considered to be collision free in most cases. The algorithm developed here, FORCE, identifies collision-free paths by using a map of the tracking area's shape and obstacles, in addition to a multistep, probabilistic prediction of the user's virtual path through a known virtual environment. In the present implementation, the path predictions describe a user's possible movements through a virtual store with aisles. Based on both the user's physical and virtual location / orientation, a search-based optimization technique identifies the optimal steering instruction given the possible user paths. Path prediction uses the map of the virtual world; consequently, the search may propose steering instructions that put the user close to walls if the user's future actions eventually lead away from the wall. Results from both simulated and real users are presented. FORCE identifies collision-free paths in 55.0 percent of the starting conditions compared to 46.1 percent for generalized methods. When considering only the conditions that result in different outcomes, redirection based on FORCE produces collision-free path 94.5 percent of the time.

In the presence of the N-heterocyclic carbene gold catalyst (NHC-AuIPr, 7), propargyl esters 1a-f and 13 undergo a [4C + 3C] cycloaddition reaction with cyclopentadiene and furan under mild conditions. The evidence suggests the formation of the seven-membered ring occurs by a direct cycloaddition process, rather than a stepwise cyclopropanation/Cope rearrangement sequence.The potent antiangiogenesis natural product family of cortistatins contain a center sevenmembered ring flanked by two six-membered rings. 1,2 Our initial attempt to construct the tetracyclic ring system using a transannular [4C+3C] cycloaddition strategy was met with mixed results. 3,4 In the same time, Mascarenas and co-workers reported an intramolecular [4C +3C] cycloaddition reaction, in which an allene functional group was selectively activated by Pt or Au catalyst. 5 This type of allene-diene intramolecular [4C+3C] cycloaddition reactions was further improved to occur under milder conditions. 6-8 Other reports using propargyl esters as reactants involved stepwise [4+3] cycloaddition reactions to prepare benzonorcaradienes and azepines. 9,10 More recently, Harmata reported the treatment of 5-silyloxydioxins with 5 mol % AuCl 3 /AgSbF 6 in the presence of cyclopentadiene or furan resulted in the formation of [4C+3C]-cycloadducts. 11 In this report, we disclose an intermolecular version of goldcatalyzed formal [4C+3C] cycloaddition reactions. This discovery expands the employment of propargyl esters as precursors in gold-catalyzed [4+3] cycloaddition reactions. 12 The likely mechanism for our recently reported gold-catalyzed transannular [4+3] cycloaddition could involve two possible pathways based on known examples in the literature. [13][14][15] The first pathway involves a gold-stabilized allyl cation and the second involves a gold carbene intermediate. As shown in Scheme 1, the first pathway (I to II through A and B) includes (1) a 3,3-rearrangement of the propargyl ester to give an allenyl ester (A), 16,17 (2) in situ activation by the same gold catalyst to generate an allyl cation B ,18 and (3) a [4+3] cycloaddition followed by a 1,2-acetoxy migration and deauration to produce the tetracyclic ring system II. The second mechanism through intermediates C and D is depicted on the right side in Scheme 1. This pathway involves a 1,2-acetoxy migration followed by a cyclopropanation/Cope rearrangement to produce the same product. Diazoesters undergo cyclopropanation/Cope rearrangement reactions in the presence of rhodium catalysts and Davies and coworkers have studied these reactions extensively. 19,20 Ohe and coworkers reported cyclopropanation of alkenes using propargylic carboxylates as vinylcarbene precursors and [RuCl 2 (CO) 3 ] 2 as the catalyst. 21 More recently, Au(I)-catalyzed Correspondence to: Benjamin W. Gung. Supplementary data Supplementary data associated with this article (experimental procedures, NMR spectra) can be found in the online version at Publisher's Disclaimer: This is a PDF file of an unedited manuscript that...

The tricyclic ring system with an oxabicyclo[3.2.1]octadiene and a fused six-membered ring was produced efficiently using the readily available propargyl ester furan substrate in the presence of a Au(I) complex. The reaction involves a tandem 3,3-rearrangement of the propargyl ester followed by an intramolecular [4+3]-cycloaddition reaction. Both the primary ligand of the gold complex (N-heterocyclic carbene; NHC) and a neutral dynamic ligand (PhCN) are important for the success of the reaction.

Gold-Catalyzed Intermolecular [4C + 3C] CycloadditionReactions. -It is demonstrated that Au-catalysts are capable of initiating the reaction of alkynes (I) with cyclic dienes. The formation of the seven-membered rings occurs by a [4 + 3] cycloaddition, rather than a stepwise cyclopropanation/Cope rearrangement sequence. Cyclopropanes (IV) can be readily transformed to (III) by Cope rearrangement in toluene under reflux (12h). The seven-membered products represent a central core of the cortistatins.