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## The Visual Display Transform in consideration of Virtual Reality

Bowling Green State University, US has reference to this Academic Journal, The Visual Display Transform in consideration of Virtual Reality Cyrus Moon Computer Integrated Surgery II (600.446) Presentation Outline Synopsis of Current Project Concepts introduced in the Reading VQS Representation Coordinate System Graph Object-to-Screen Transform Relevancy of concepts so that the current project Current Project: Image/Video Overlay Image Overlay: -the merging of relevant computer generated information alongside the user?s actual view of the real world Video Overlay: -the merging of relevant computer generated information alongside display output from a video source

Related University That Contributed for this Journal are Acknowledged in the above Image

Relevant Concepts Registration Tracking in 3D real space 3D modeling/rendering Frame transformations Background Reading Robinett Warren, Halloway Richard. The Visual Display Transformation in consideration of Virtual Reality. Technical Report TR94-031 (1994), Dept. of Computer Science, University of North Carolina at Chapel Hill. VQS – Vector Quaternion Scalar Representation (for frame transformations) Vector(v) (3 terms) ? displacement Quaternion(q) (4 terms) ? rotation Scalar(s) (1 term) ? uniform scaling [ (vx, vy, vz), (qx, qy, qz, qw), s ]

Advantages of VQS (over the Euler 4×4 homogeneous matrix) Translation, rotation, in addition to scaling components are separated Renormalizing the rotation is simpler (since rotation in addition to scaling are separate) Uniform scaling in the virtual world a useful operation Quaternions a better method of manipulating 3D rotations than Euler rotations Advantages of the Quaternion (over the Euler 3×3 Rotation Matrix) Fewer components (4 instead of 9); fewer redundant parameters More elegant, numerically robust Explicit representation of the angle in addition to axis of rotation Allows easy interpolation between two orientations The Quaternion [(qx, qy, qz), qw] (qx, qy, qz) ? axis of rotation qw ? angle of rotation: qw takes values from ?1 so that 1

Phase Equilibrium Makaopuhi Lava Lake Makaopuhi Lava Lake Makaopuhi Lava Lake Makaopuhi Lava Lake Crystallization Behavior of Melts The Phase Rule One Component Systems One Component Systems Two Component Systems Two Component Systems

Quaternion Math Addition: Multiplication: Multiplication by Scalar: Quaternion Math (cont?d) Taking the norm: Normalization: Inversion: Interpolation: Using Quaternions Rotation of a vector p by quaternion q: pnew = q*p*q-1 -the vector p is treated as a quaternion w/ 0 as the 4th (scalar) term -the result will always have a 4th term of 0, as well

VQS Math Conversion so that 4×4 Matrix: [v,q,s] = Mtranslate * Mrotate * Mscale = Using VQS Transforms Transformation of a vector (p) alongside VQS: p? = [v, q, s]*p = s(q*p*q-1) + v Composition of two VQS transforms: TA_B*TB_C = [vA_B,qA_B,sA_B]*[vB_C,qB_C,sB_C] = [(sA_B*(qA_B*vB_C*qA_B)-1) + vA_B, qA_B*qB_C, sA_B*sB_C] Inverse of a VQS Transform: TA_B-1 = [vA_B, qA_B, sA_B]-1 = [1/sA_B*(qA_B-1*(-vA_B)*qA_B), qA_B-1, 1/sA_B] The Coordinate System Graph Robinett & Halloway

The Coordinate System Graph Representation: Each Node represents a coordinate system Each line represents some kind of independent transformation Properties: Connected: each node is connected alongside every other node Acyclic: there is only one pathway between any two given nodes Transformations Independent: characterized by being independent variables within the software Measured by tracker Constant (rigid) Dependent: calculated from independent transforms The Coordinate System Graph: -intuitively organizes all independent transforms in addition to coordinate systems; easily expandable -allows easy calculation of any dependent transform present within the VR system The Object-to-Screen Transform TS_O = TS_US * TUS_N * TN_E * TE_H * TH_HS * THS_TB * TTB_R * TR_W * TW_O -TB_A is defined as the transformation from frame A so that B S = Screen HS = Head Sensor US = Undistorted Screen TB = Tracker Base N = Normalized R = Room E = Eye W = World H = Head O = Object

TW_O: World_Object ? object in the virtual world. v – position q – orientation s – size TR_W: Room_World ? the user position in the virtual world v – position q – tilt of the world s – user’s size (shrinking or expanding of the world) TTB_R: TrackerBase_Room ? position of tracker base (stored in calibration file) s – must always be one (both cs?s in real-space) Pre-calculated VQS Transforms THS_TB: HeadSensor_TrackerBase ? inverse of the head position in addition to orientation read from tracker s = 1 TTH_HS: Head_HeadSensor ? position in addition to orientation of the HMD sensor w/ respect so that the head (center of the eyes) s = 1 Pre-calculated TE_H: Eye_Head ? position/orientation of head coordinate system w/ respect so that each eye v ? different in consideration of each user (though a default value can be used q ? dependent on orientation of HMD displays s = 1 Pre-calculated VQS Transforms (cont?d) TEye_Head Robinett & Halloway

TN_E: Normalized_Eye ? perspective projection, normalization Three so that two dimensions (projection of world onto viewing plane) TUS_N: UndistortedScreen_Normalized? conversion so that pixel coordinates Simple scaling process TS_US: Screen_UndistortedScreen ? correction of image distortion Non-VQS Transforms Applicable Concepts VQS Representation Tracker Data ? Transform calculations Registration Transforms (non-deformable objects) Elimination of the possibility of warping Coordinate System Graph Other concepts discussed in the individual transforms Example: perspective transform Coordinate Graph (Video Overlay) Patient markers Model (from Imaging) World (Tracker) Tool 1 Tool k . . . . . . . . Camera Lens Screen

Coordinate Graph (Image Overlay) Patient markers Model (from Imaging) World (Tracker) Tool 1 Tool k . . . . . . . . Silvered Glass Head Virtual Projection Plane Screen

## Dufresne, Chris Host

Dufresne, Chris is from United States and they belong to Host and work for KPXQ-AM in the AZ state United States got related to this Particular Article.

## Journal Ratings by Bowling Green State University

This Particular Journal got reviewed and rated by Coordinate Graph (Image Overlay) Patient markers Model (from Imaging) World (Tracker) Tool 1 Tool k . . . . . . . . Silvered Glass Head Virtual Projection Plane Screen and short form of this particular Institution is US and gave this Journal an Excellent Rating.