Color space mapping for intuitive surface normal visualization
A color mapping technique that provides an intuitive visualization of surface normals is described. The surface normals can be associated with a mesh for a virtual object to be displayed in augmented reality. The color mapping technique can map a unit sphere in a color space to an octahedron. The vertices of the octahedron can be aligned with prime colors of the color space. To perform the alignment, a rotation and shear matrix can be determined from coordinates for octahedron positions and coordinates of colors in the color space. The rotation and shear can provide that each region of the unit color sphere is dominated by a single prime color, with gradients between prime colors being visually balanced. Surface normals of a mesh for a virtual object can be visualized using the color mapping, and a viewer can readily determine how distant in terms of rotation two surface normals are from each other.
1. A method comprising:
under control of hardware computing circuitry:
mapping a unit sphere in a color space to an octahedron;
aligning the octahedron with prime colors of the color space to provide an aligned octahedron, wherein aligning the octahedron comprises determining a rotation and shear matrix; and
outputting a color mapping associated with the aligned octahedron.
2. The method of claim 1 , wherein the color space comprises a red, green, blue (RGB) color space, a hue, saturation, value (HSV) color space, a CIE Lab color space, or a National Television System Committee (NTSC) color space.
3. The method of claim 1 , wherein the prime colors comprise three primary colors and three secondary colors of the color space.
4. The method of claim 1 , wherein the prime colors comprise red, green, blue, cyan, magenta, and yellow.
5. The method of claim 1 , wherein mapping the unit sphere comprises an area-preserving mapping.
6. The method of claim 1 , wherein mapping the unit sphere comprises mapping a point (x, y, z) on the unit sphere to a point (X, Y, Z) on the octahedron according to:
X
=
sgn
(
x
)
L
2
π
1
-
|
z
|
(
π
-
2
arctan
|
y
|
|
x
|
)
,
Y
=
sgn
(
y
)
L
2
π
1
-
|
z
|
•2arctan
|
y
|
|
x
|
,
Z
=
sgn
(
z
)
L
2
(
1
-
1
-
|
z
|
)
.
7. The method of claim 1 , wherein aligning the octahedron comprises aligning each vertex of the octahedron with a prime color of the color space.
8. The method of claim 1 , wherein aligning the octahedron comprises identifying analogous colors of the color space with neighboring vertices of the octahedron.
9. The method of claim 1 , wherein aligning the octahedron comprises not identifying complementary colors of the color space with neighboring vertices of the octahedron.
10. The method of claim 1 , wherein aligning the octahedron comprises determining a six-dimensional (6D) list comprising three-dimensional (3D) coordinates for positions on the octahedron and 3D coordinates of the color space.
11. The method of claim 1 , wherein determining the rotation and shear matrix comprises utilizing a least squares technique.
12. The method of claim 1 , wherein the rotation and shear matrix provides that each vertex of the octahedron touches a specified number of corners of a unit cube.
13. The method of claim 1 , further comprising applying the color mapping to a surface normal.
14. The method of claim 13 , wherein the surface normal is associated with a mesh for a virtual object.
15. The method of claim 1 , further comprising utilizing the color mapping to generate a visualization of surface normals.
16. A system comprising:
hardware computing circuitry configured to:
map a unit sphere in a color space to an octahedron;
align the octahedron with prime colors of the color space to provide an aligned octahedron, wherein aligning the octahedron comprises determining a rotation and shear matrix; and
output a color mapping associated with the aligned octahedron.
17. The system of claim 16 , wherein to map the unit sphere the hardware circuitry is configured to utilize an area-preserving mapping.
18. The system of claim 16 , wherein to map the unit sphere, the hardware circuitry is configured to map a point (x, y, z) on the unit sphere to a point (X, Y, Z) on the octahedron according to:
X
=
sgn
(
x
)
L
2
π
1
-
|
z
|
(
π
-
2
arctan
|
y
|
|
x
|
)
,
Y
=
sgn
(
y
)
L
2
π
1
-
|
z
|
•2arctan
|
y
|
|
x
|
,
Z
=
sgn
(
z
)
L
2
(
1
-
1
-
|
z
|
)
.
19. The system of claim 18 , wherein the hardware circuitry is further configured to apply the color mapping to a surface normal.