hrtfs can be calculated
DESCRIPTION
HRTFs can be calculated. Wave equation:. Fourier Transform from Time to Frequency Domain. Helmholtz equation:. Boundary conditions:. Sound-hard boundaries:. Sound-soft boundaries:. Impedance boundary conditions:. Sommerfeld radiation condition (for infinite domains):. - PowerPoint PPT PresentationTRANSCRIPT
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HRTFs can be calculated
0P
n
2 2 0P k P
Sound-hard boundaries:
Sound-soft boundaries: 0P
Impedance boundary conditions:P
i P gn
Sommerfeld radiation condition (for infinite domains): lim 0
r
Pr ikP
r
Helmholtz equation:
Boundary conditions:
2 2 2 22 2 2
2 2 2 2
' ' ' ''
p p p pc c p
t x y z
Wave equation:
Fourier Transform from Time to Frequency Domain
'( , , , ) ( , , ; ) i tp x y z t P x y z e d
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HRTFs can be computed• Boundary Element Method• Obtain a mesh• Using Green’s function G
• Convert equation and b.c.s to an integral equation
• Need accurate surface meshes of individuals• Obtain these via computer vision
, ;, ;
y
yy y
p y G x y kC x p x G x y k p y d
n n
,4
ikeG
x y
x yx y
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Current work: Develop Meshes
Original Kemar surface points from Dr. Yuvi Kahana,ISVR, Southampton, UK
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New quadric metric for simplifying meshes with appearance attributes
Hugues HoppeMicrosoft Research
Presented by Zhihui Tang
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Introduction• Several techniques have been developed for
geometrically simplify them. Relatively few techniques account for appearance attributes during simplification.
• Metric introduced by Garland and Hecbert is fast and reasonably accurate. They can deal with appearance attribute.
• In this paper, developed an improved quadric error metric for simplifying meshes with attributes.
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Advantage of the new metric:
• intuitively measures error by geometric correspondence
• less storage (linear on no. of attributes)
• evaluate fast (sparse quadric matrix)
• more accurate simplifications(experiments)
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What is Triangle Meshes
Vertex 1 xVertex 1 x11 y y11 z z11 Face 1 1 Face 1 1 2 32 3
Vertex 2 xVertex 2 x22 y y22 z z22 Face 2 1 Face 2 1 2 4 2 4
Vertex 3 xVertex 3 x33 y y33 z z33 Face 3 2 Face 3 2 4 54 5
………… …………
• Geometry Geometry pp R R33
• attributesattributes normalsnormals, , colorscolors, , texture coordstexture coords, ..., ...
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Notation
• A triangle mesh M is described by:
V , F.
• Each vertex v in V has a geometric position pv in R3 and A set of m attribute scalars sv in Rm. That is v is in Rm+3.
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Previous Quadratic Error Metrics
• Minimize sum of squared distances to planes(illustration in 2D)(illustration in 2D)
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Mesh simplification
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Simplification of Geometry
Qv(v) = Qv1(v)+Qv2(v)
Qf(v=(p))=(ntv+d)2=vt(nnt)v+2dntv+d2
=(A,b,c)=((nnt),(dn),d2)
Qf is stored using 10 coefficients.
Vertex position vmin minimizing Qv(v) is the solution
of Av = -b
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Simplification of Geometry and Attributes
• This approach is to generalize the distances-to-plane metric in R3 to a distance-to- hyperplane in R3+m.
• Qf(v)=||v-v’||2 =||p-p’||2+||s-s’||2
• Storage requires (4+m)(5+m)/2 coefficients
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New Quadric Error Metric
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New Quadric Error Metric
• Qf(v)=||p-p’||2+||s-s’||2
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(A,b,c) =
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Storage Comparison
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Experiment
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Attribute DiscontinuitiesExample: a crease ,intensities.
Modeling such discontinuities needs store multiple sets of attribute values per vertex.
Wedges are very useful in this context.
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Wedge
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Wedge(II)
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Wedge unification
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Simplification Enhancements
• Memoryless simplification
• Volume preservation
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Memoryless simplification
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Volume preservation(I)
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Volume preservation(II)
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Results(I)
• Distance between two meshes M1 and M2 is obtained by sampling a collection of points from M1and measuring the distances to the closest points on M2 plus the distances of the same number of points from M2 to M1
• Statistics are reported using L2 norm and L-infinity norm
• For meshes with attributes, we also sample attributes at the same points and measure the divisions from the values linearly interpolated at the closest point on the other mesh.
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Results(II)
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Mesh with color
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Results(IV)
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Results (V)
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Mesh with normals
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Wedge Attributes
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Radiosity solution
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Results (VI)