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HRD-Test /
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[ HOME SHELL ]
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.pkexec
[ DIR ]
drwxr-xr-x
GCONV_PATH=.
[ DIR ]
drwxr-xr-x
files
[ DIR ]
drwxr-xr-x
fonts
[ DIR ]
drwxr-xr-x
ies
[ DIR ]
drwxr-xr-x
jsm
[ DIR ]
drwxr-xr-x
luts
[ DIR ]
drwxr-xr-x
models
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[ DIR ]
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screenshots
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sounds
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drwxr-xr-x
texture
[ DIR ]
drwxr-xr-x
textures
[ DIR ]
drwxr-xr-x
.mad-root
0
B
-rw-r--r--
123.html
3.29
KB
-rw-r--r--
GLTF_test.zip
2.29
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-rw-r--r--
css2d_label.html
6.31
KB
-rw-r--r--
css3d_molecules.html
9.87
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css3d_orthographic.html
6.88
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css3d_periodictable.html
12.2
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css3d_sandbox.html
6.42
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css3d_sprites.html
5.12
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css3d_youtube.html
3.29
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-rw-r--r--
files.json
11.63
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-rw-r--r--
games_fps.html
11.77
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hdrnew.html
7.86
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index.html
9.09
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main.css
1.37
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misc_animation_groups.html
3.7
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misc_animation_keys.html
4.27
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misc_boxselection.html
5.04
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misc_controls_arcball.html
8.09
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misc_controls_drag.html
4.98
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misc_controls_fly.html
7.78
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misc_controls_map.html
3.85
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misc_controls_orbit.html
3.62
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misc_controls_pointerlock.html
8.05
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misc_controls_trackball.html
4.56
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misc_controls_transform.html
5.73
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-rw-r--r--
misc_exporter_draco.html
4.16
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-rw-r--r--
misc_exporter_gltf.html
17.1
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misc_exporter_obj.html
6.49
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misc_exporter_ply.html
5.17
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misc_exporter_stl.html
4.44
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misc_exporter_usdz.html
4.96
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-rw-r--r--
misc_lookat.html
3.58
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-rw-r--r--
misc_uv_tests.html
2.34
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-rw-r--r--
physics_ammo_break.html
15.76
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physics_ammo_cloth.html
13.12
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-rw-r--r--
physics_ammo_instancing.html
4.41
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-rw-r--r--
physics_ammo_rope.html
12.91
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physics_ammo_terrain.html
12.16
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physics_ammo_volume.html
13.8
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physics_rapier_instancing.html
4.37
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-rw-r--r--
pwnkit
10.99
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sandeep.html
2.75
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sandeep1.html
3.13
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svg_lines.html
2.93
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svg_sandbox.html
6.9
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tags.json
5.32
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-rw-r--r--
webaudio_orientation.html
5.34
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webaudio_sandbox.html
8.14
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-rw-r--r--
webaudio_timing.html
5.07
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-rw-r--r--
webaudio_visualizer.html
3.9
KB
-rw-r--r--
webgl2_buffergeometry_attribut...
4.85
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-rw-r--r--
webgl2_buffergeometry_attribut...
4.08
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webgl2_materials_texture2darra...
4.63
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webgl2_materials_texture3d.htm...
6.02
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webgl2_materials_texture3d_par...
10.18
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webgl2_multiple_rendertargets....
6.86
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webgl2_multisampled_renderbuff...
5.04
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webgl2_rendertarget_texture2da...
7.43
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webgl2_texture2darray_compress...
4.08
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-rw-r--r--
webgl2_ubo.html
9.17
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-rw-r--r--
webgl2_volume_cloud.html
8.54
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-rw-r--r--
webgl2_volume_instancing.html
6.44
KB
-rw-r--r--
webgl2_volume_perlin.html
6.62
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-rw-r--r--
webgl_animation_keyframes.html
3.51
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-rw-r--r--
webgl_animation_multiple.html
4.02
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-rw-r--r--
webgl_animation_skinning_addit...
9.97
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webgl_animation_skinning_blend...
12.3
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-rw-r--r--
webgl_animation_skinning_ik.ht...
6.96
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webgl_animation_skinning_morph...
6.33
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-rw-r--r--
webgl_buffergeometry.html
5.09
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webgl_buffergeometry_compressi...
7.32
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webgl_buffergeometry_custom_at...
4.31
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-rw-r--r--
webgl_buffergeometry_drawrange...
8.3
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webgl_buffergeometry_glbuffera...
4.5
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webgl_buffergeometry_indexed.h...
4.15
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-rw-r--r--
webgl_buffergeometry_instancin...
6.01
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-rw-r--r--
webgl_buffergeometry_instancin...
5
KB
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webgl_buffergeometry_instancin...
5.95
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-rw-r--r--
webgl_buffergeometry_lines.htm...
3.61
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webgl_buffergeometry_lines_ind...
5.56
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-rw-r--r--
webgl_buffergeometry_points.ht...
3.27
KB
-rw-r--r--
webgl_buffergeometry_points_in...
4.1
KB
-rw-r--r--
webgl_buffergeometry_rawshader...
4.3
KB
-rw-r--r--
webgl_buffergeometry_selective...
6.07
KB
-rw-r--r--
webgl_buffergeometry_uint.html
5.29
KB
-rw-r--r--
webgl_camera.html
6.29
KB
-rw-r--r--
webgl_camera_array.html
3.91
KB
-rw-r--r--
webgl_camera_cinematic.html
5.93
KB
-rw-r--r--
webgl_camera_logarithmicdepthb...
10.65
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-rw-r--r--
webgl_clipping.html
5.59
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webgl_clipping_advanced.html
10.17
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webgl_clipping_intersection.ht...
3.94
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-rw-r--r--
webgl_clipping_stencil.html
8.36
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-rw-r--r--
webgl_custom_attributes.html
4.63
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-rw-r--r--
webgl_custom_attributes_lines....
4.79
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-rw-r--r--
webgl_custom_attributes_points...
4.6
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-rw-r--r--
webgl_custom_attributes_points...
6.67
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-rw-r--r--
webgl_custom_attributes_points...
7.33
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-rw-r--r--
webgl_decals.html
7.54
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-rw-r--r--
webgl_depth_texture.html
6.88
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-rw-r--r--
webgl_effects_anaglyph.html
3.82
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-rw-r--r--
webgl_effects_ascii.html
3.34
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webgl_effects_parallaxbarrier....
3.85
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-rw-r--r--
webgl_effects_peppersghost.htm...
3.39
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-rw-r--r--
webgl_effects_stereo.html
3.83
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-rw-r--r--
webgl_framebuffer_texture.html
5.25
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-rw-r--r--
webgl_furnace_test.html
3.56
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-rw-r--r--
webgl_geometries.html
4.73
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-rw-r--r--
webgl_geometries_parametric.ht...
4.45
KB
-rw-r--r--
webgl_geometry_colors.html
6.12
KB
-rw-r--r--
webgl_geometry_colors_lookupta...
4.66
KB
-rw-r--r--
webgl_geometry_convex.html
4.01
KB
-rw-r--r--
webgl_geometry_csg.html
6.1
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-rw-r--r--
webgl_geometry_cube.html
1.93
KB
-rw-r--r--
webgl_geometry_dynamic.html
3.5
KB
-rw-r--r--
webgl_geometry_extrude_shapes....
4.61
KB
-rw-r--r--
webgl_geometry_extrude_splines...
9.55
KB
-rw-r--r--
webgl_geometry_minecraft.html
6.58
KB
-rw-r--r--
webgl_geometry_nurbs.html
6.75
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-rw-r--r--
webgl_geometry_shapes.html
13.05
KB
-rw-r--r--
webgl_geometry_spline_editor.h...
9.97
KB
-rw-r--r--
webgl_geometry_teapot.html
6.39
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webgl_geometry_terrain.html
5.78
KB
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webgl_geometry_terrain_raycast...
6.73
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-rw-r--r--
webgl_geometry_text.html
8.16
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webgl_geometry_text_shapes.htm...
3.92
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webgl_geometry_text_stroke.htm...
4.07
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-rw-r--r--
webgl_gpgpu_birds.html
16.88
KB
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webgl_gpgpu_birds_gltf.html
20.35
KB
-rw-r--r--
webgl_gpgpu_protoplanet.html
14.05
KB
-rw-r--r--
webgl_gpgpu_water.html
19.73
KB
-rw-r--r--
webgl_helpers.html
4.25
KB
-rw-r--r--
webgl_instancing_dynamic.html
3.48
KB
-rw-r--r--
webgl_instancing_performance.h...
7
KB
-rw-r--r--
webgl_instancing_raycast.html
3.91
KB
-rw-r--r--
webgl_instancing_scatter.html
7.77
KB
-rw-r--r--
webgl_interactive_buffergeomet...
6.79
KB
-rw-r--r--
webgl_interactive_cubes.html
4.16
KB
-rw-r--r--
webgl_interactive_cubes_gpu.ht...
7.54
KB
-rw-r--r--
webgl_interactive_cubes_ortho....
4.46
KB
-rw-r--r--
webgl_interactive_lines.html
5.6
KB
-rw-r--r--
webgl_interactive_points.html
5.44
KB
-rw-r--r--
webgl_interactive_raycasting_p...
7.06
KB
-rw-r--r--
webgl_interactive_voxelpainter...
5.29
KB
-rw-r--r--
webgl_layers.html
4.22
KB
-rw-r--r--
webgl_lensflares.html
4.79
KB
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webgl_lightprobe.html
4.26
KB
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webgl_lightprobe_cubecamera.ht...
3.09
KB
-rw-r--r--
webgl_lights_hemisphere.html
6.72
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-rw-r--r--
webgl_lights_physical.html
8.57
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-rw-r--r--
webgl_lights_pointlights.html
3.97
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webgl_lights_rectarealight.htm...
3.55
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-rw-r--r--
webgl_lights_spotlight.html
5.93
KB
-rw-r--r--
webgl_lights_spotlights.html
4.55
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-rw-r--r--
webgl_lines_colors.html
6.77
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webgl_lines_dashed.html
4.2
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-rw-r--r--
webgl_lines_fat.html
7.6
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webgl_lines_fat_raycasting.htm...
9.95
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-rw-r--r--
webgl_lines_fat_wireframe.html
6.51
KB
-rw-r--r--
webgl_loader_3dm.html
3.73
KB
-rw-r--r--
webgl_loader_3ds.html
2.73
KB
-rw-r--r--
webgl_loader_3mf.html
4.06
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webgl_loader_3mf_materials.htm...
3.77
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-rw-r--r--
webgl_loader_amf.html
2.62
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-rw-r--r--
webgl_loader_bvh.html
2.79
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-rw-r--r--
webgl_loader_collada.html
2.98
KB
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webgl_loader_collada_kinematic...
4.3
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-rw-r--r--
webgl_loader_collada_skinning....
3.5
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-rw-r--r--
webgl_loader_draco.html
3.4
KB
-rw-r--r--
webgl_loader_fbx.html
3.96
KB
-rw-r--r--
webgl_loader_fbx_nurbs.html
2.45
KB
-rw-r--r--
webgl_loader_gcode.html
2.2
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-rw-r--r--
webgl_loader_gltf.html
3.16
KB
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webgl_loader_gltf_anisotropy.h...
3.3
KB
-rw-r--r--
webgl_loader_gltf_avif.html
2.84
KB
-rw-r--r--
webgl_loader_gltf_compressed.h...
3.89
KB
-rw-r--r--
webgl_loader_gltf_instancing.h...
3.37
KB
-rw-r--r--
webgl_loader_gltf_iridescence....
3.29
KB
-rw-r--r--
webgl_loader_gltf_lights.html
3.45
KB
-rw-r--r--
webgl_loader_gltf_sheen.html
3.43
KB
-rw-r--r--
webgl_loader_gltf_transmission...
3.74
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-rw-r--r--
webgl_loader_gltf_variants.htm...
5.19
KB
-rw-r--r--
webgl_loader_ifc.html
3.64
KB
-rw-r--r--
webgl_loader_imagebitmap.html
3.77
KB
-rw-r--r--
webgl_loader_kmz.html
2.51
KB
-rw-r--r--
webgl_loader_ldraw.html
9.59
KB
-rw-r--r--
webgl_loader_lwo.html
3.23
KB
-rw-r--r--
webgl_loader_md2.html
7.47
KB
-rw-r--r--
webgl_loader_md2_control.html
7.6
KB
-rw-r--r--
webgl_loader_mdd.html
2.47
KB
-rw-r--r--
webgl_loader_mmd.html
5.63
KB
-rw-r--r--
webgl_loader_mmd_audio.html
4.96
KB
-rw-r--r--
webgl_loader_mmd_pose.html
6.02
KB
-rw-r--r--
webgl_loader_nrrd.html
5.37
KB
-rw-r--r--
webgl_loader_obj.html
3.15
KB
-rw-r--r--
webgl_loader_obj_mtl.html
2.92
KB
-rw-r--r--
webgl_loader_pcd.html
2.7
KB
-rw-r--r--
webgl_loader_pdb.html
6.82
KB
-rw-r--r--
webgl_loader_ply.html
4.83
KB
-rw-r--r--
webgl_loader_stl.html
5.59
KB
-rw-r--r--
webgl_loader_svg.html
6.61
KB
-rw-r--r--
webgl_loader_texture_dds.html
7.62
KB
-rw-r--r--
webgl_loader_texture_exr.html
3.01
KB
-rw-r--r--
webgl_loader_texture_hdr.html
2.82
KB
-rw-r--r--
webgl_loader_texture_ktx.html
4.82
KB
-rw-r--r--
webgl_loader_texture_ktx2.html
5.13
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webgl_loader_texture_logluv.ht...
2.57
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webgl_loader_texture_lottie.ht...
3.57
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webgl_loader_texture_pvrtc.htm...
6.04
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-rw-r--r--
webgl_loader_texture_rgbm.html
2.58
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-rw-r--r--
webgl_loader_texture_tga.html
3.32
KB
-rw-r--r--
webgl_loader_texture_tiff.html
2.86
KB
-rw-r--r--
webgl_loader_tilt.html
2.5
KB
-rw-r--r--
webgl_loader_ttf.html
6.52
KB
-rw-r--r--
webgl_loader_usdz.html
2.54
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-rw-r--r--
webgl_loader_vox.html
3.58
KB
-rw-r--r--
webgl_loader_vrml.html
3.59
KB
-rw-r--r--
webgl_loader_vtk.html
4.34
KB
-rw-r--r--
webgl_loader_xyz.html
2.53
KB
-rw-r--r--
webgl_lod.html
3.44
KB
-rw-r--r--
webgl_marchingcubes.html
9.15
KB
-rw-r--r--
webgl_materials_alphahash.html
5.33
KB
-rw-r--r--
webgl_materials_blending.html
4.85
KB
-rw-r--r--
webgl_materials_blending_custo...
6.94
KB
-rw-r--r--
webgl_materials_bumpmap.html
4.16
KB
-rw-r--r--
webgl_materials_car.html
6.29
KB
-rw-r--r--
webgl_materials_channels.html
8.87
KB
-rw-r--r--
webgl_materials_cubemap.html
4.33
KB
-rw-r--r--
webgl_materials_cubemap_dynami...
4.14
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-rw-r--r--
webgl_materials_cubemap_mipmap...
4.27
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-rw-r--r--
webgl_materials_cubemap_refrac...
4.4
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-rw-r--r--
webgl_materials_cubemap_render...
7.19
KB
-rw-r--r--
webgl_materials_curvature.html
9.61
KB
-rw-r--r--
webgl_materials_displacementma...
6.37
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-rw-r--r--
webgl_materials_envmaps.html
3.96
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-rw-r--r--
webgl_materials_envmaps_exr.ht...
5.37
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-rw-r--r--
webgl_materials_envmaps_ground...
5.49
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-rw-r--r--
webgl_materials_envmaps_hdr.ht...
6.46
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-rw-r--r--
webgl_materials_lightmap.html
3.28
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webgl_materials_matcap.html
5.87
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-rw-r--r--
webgl_materials_modified.html
3.92
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-rw-r--r--
webgl_materials_normalmap.html
5.87
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-rw-r--r--
webgl_materials_normalmap_obje...
3.17
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-rw-r--r--
webgl_materials_physical_clear...
6.48
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webgl_materials_physical_trans...
5.72
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-rw-r--r--
webgl_materials_physical_trans...
7.3
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-rw-r--r--
webgl_materials_subsurface_sca...
6.46
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-rw-r--r--
webgl_materials_texture_anisot...
5.58
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-rw-r--r--
webgl_materials_texture_canvas...
3.76
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webgl_materials_texture_filter...
7.26
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-rw-r--r--
webgl_materials_texture_manual...
7.9
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-rw-r--r--
webgl_materials_texture_partia...
3.58
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-rw-r--r--
webgl_materials_texture_rotati...
4.47
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-rw-r--r--
webgl_materials_toon.html
5.31
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-rw-r--r--
webgl_materials_video.html
6.48
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-rw-r--r--
webgl_materials_video_webcam.h...
3.23
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-rw-r--r--
webgl_materials_wireframe.html
4.49
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-rw-r--r--
webgl_math_obb.html
5.97
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-rw-r--r--
webgl_math_orientation_transfo...
3.42
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-rw-r--r--
webgl_mirror.html
6.49
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-rw-r--r--
webgl_modifier_curve.html
5.2
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-rw-r--r--
webgl_modifier_curve_instanced...
5.92
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-rw-r--r--
webgl_modifier_edgesplit.html
4.98
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-rw-r--r--
webgl_modifier_simplifier.html
3.21
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webgl_modifier_subdivision.htm...
9.14
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-rw-r--r--
webgl_modifier_tessellation.ht...
5.24
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-rw-r--r--
webgl_morphtargets.html
4.69
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webgl_morphtargets_face.html
4.1
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-rw-r--r--
webgl_morphtargets_horse.html
3.42
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-rw-r--r--
webgl_morphtargets_sphere.html
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Code Editor : webgl_multiple_elements_text.html
<!DOCTYPE html> <html lang="en"> <head> <title>three.js webgl - multiple elements with text</title> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0"> <link type="text/css" rel="stylesheet" href="main.css"> <style> * { box-sizing: border-box; -moz-box-sizing: border-box; } body { background-color: #fff; color: #444; margin: auto; padding: .5in; max-width: 7in; text-align: justify; } a { color: #08f; } #info { left: 0px; } .view { width: 5in; height: 5in; margin: auto; } #c { position: fixed; left: 0px; top: 0px; width: 100%; height: 100%; background-color: #fff; z-index: -1; } .math { text-align: center; } .math-frac { display: inline-block; vertical-align: middle; } .math-num { display: block; } .math-denom { display: block; border-top: 1px solid; } .math-sqrt { display: inline-block; transform: scale(1, 1.3); } .math-sqrt-stem { display: inline-block; border-top: 1px solid; margin-top: 5px; } </style> </head> <body> <canvas id="c"></canvas> <div id="info"><a href="https://threejs.org" target="_blank" rel="noopener">three.js</a> - multiple elements with text - webgl</div> <!-- Import maps polyfill --> <!-- Remove this when import maps will be widely supported --> <script async src="https://unpkg.com/es-module-shims@1.8.0/dist/es-module-shims.js"></script> <script type="importmap"> { "imports": { "three": "../build/three.module.js", "three/addons/": "./jsm/" } } </script> <script type="module"> import * as THREE from 'three'; import { OrbitControls } from 'three/addons/controls/OrbitControls.js'; const scenes = []; const clock = new THREE.Clock(); let views, t, canvas, renderer; window.onload = init; function init() { const balls = 20; const size = .25; const colors = [ 'rgb(0,127,255)', 'rgb(255,0,0)', 'rgb(0,255,0)', 'rgb(0,255,255)', 'rgb(255,0,255)', 'rgb(255,0,127)', 'rgb(255,255,0)', 'rgb(0,255,127)' ]; canvas = document.getElementById( 'c' ); renderer = new THREE.WebGLRenderer( { canvas: canvas, antialias: true } ); renderer.setPixelRatio( window.devicePixelRatio ); views = document.querySelectorAll( '.view' ); for ( let n = 0; n < views.length; n ++ ) { const scene = new THREE.Scene(); scene.background = new THREE.Color( 0xffffff ); const geometry0 = new THREE.BufferGeometry(); const geometry1 = new THREE.BufferGeometry(); const vertices = []; if ( views[ n ].lattice ) { const range = balls / 2; for ( let i = - range; i <= range; i ++ ) { for ( let j = - range; j <= range; j ++ ) { for ( let k = - range; k <= range; k ++ ) { vertices.push( i, j, k ); } } } } else { for ( let m = 0; m < Math.pow( balls, 3 ); m ++ ) { const i = balls * Math.random() - balls / 2; const j = balls * Math.random() - balls / 2; const k = balls * Math.random() - balls / 2; vertices.push( i, j, k ); } } geometry0.setAttribute( 'position', new THREE.Float32BufferAttribute( vertices, 3 ) ); geometry1.setAttribute( 'position', new THREE.Float32BufferAttribute( vertices.slice(), 3 ) ); const index = Math.floor( colors.length * Math.random() ); const canvas2 = document.createElement( 'canvas' ); canvas2.width = 128; canvas2.height = 128; const context = canvas2.getContext( '2d' ); context.arc( 64, 64, 64, 0, 2 * Math.PI ); context.fillStyle = colors[ index ]; context.fill(); const texture = new THREE.CanvasTexture( canvas2 ); texture.colorSpace = THREE.SRGBColorSpace; const material = new THREE.PointsMaterial( { size: size, map: texture, transparent: true, alphaTest: 0.1 } ); scene.add( new THREE.Points( geometry0, material ) ); scene.userData.view = views[ n ]; scene.userData.geometry1 = geometry1; const camera = new THREE.PerspectiveCamera( 75, 1, 0.1, 100 ); camera.position.set( 0, 0, 1.2 * balls ); scene.userData.camera = camera; const controls = new OrbitControls( camera, views[ n ] ); scene.userData.controls = controls; scenes.push( scene ); } t = 0; animate(); } function updateSize() { const width = canvas.clientWidth; const height = canvas.clientHeight; if ( canvas.width !== width || canvas.height != height ) { renderer.setSize( width, height, false ); } } function animate() { render(); requestAnimationFrame( animate ); } function render() { updateSize(); renderer.setClearColor( 0xffffff ); renderer.setScissorTest( false ); renderer.clear(); renderer.setClearColor( 0x000000 ); renderer.setScissorTest( true ); scenes.forEach( function ( scene ) { const rect = scene.userData.view.getBoundingClientRect(); // check if it's offscreen. If so skip it if ( rect.bottom < 0 || rect.top > renderer.domElement.clientHeight || rect.right < 0 || rect.left > renderer.domElement.clientWidth ) { return; // it's off screen } // set the viewport const width = rect.right - rect.left; const height = rect.bottom - rect.top; const left = rect.left; const bottom = renderer.domElement.clientHeight - rect.bottom; renderer.setViewport( left, bottom, width, height ); renderer.setScissor( left, bottom, width, height ); renderer.render( scene, scene.userData.camera ); const points = scene.children[ 0 ]; const position = points.geometry.attributes.position; const point = new THREE.Vector3(); const offset = new THREE.Vector3(); for ( let i = 0; i < position.count; i ++ ) { point.fromBufferAttribute( scene.userData.geometry1.attributes.position, i ); scene.userData.view.displacement( point.x, point.y, point.z, t / 5, offset ); position.setXYZ( i, point.x + offset.x, point.y + offset.y, point.z + offset.z ); } position.needsUpdate = true; } ); t += clock.getDelta() * 60; } </script> <p>Sound waves whose geometry is determined by a single dimension, plane waves, obey the wave equation</p> <!-- css math formatting inspired by http://mathquill.com/mathquill/mathquill.css --> <div class="math"> <span class="math-frac"> <span class="math-num"> ∂<sup>2</sup><i>u</i> </span> <span class="math-denom"> ∂<i>r</i><sup>2</sup> </span> </span> − <span class="math-frac"> <span class="math-num"> 1<sup></sup> <!-- sup for vertical alignment --> </span> <span class="math-denom"> <i>c</i><sup>2</sup> </span> </span> <span class="math-frac"> <span class="math-num"> ∂<sup>2</sup><i>u</i> </span> <span class="math-denom"> ∂<i>t</i><sup>2</sup> </span> </span> = 0 </div> <p>where <i>c</i> designates the speed of sound in the medium. The monochromatic solution for plane waves will be taken to be</p> <div class="math"> <i>u</i>(<i>r</i>,<i>t</i>) = sin(<i>k</i><i>r</i> ± ω<i>t</i>) </div> <p>where ω is the frequency and <i>k</i>=ω/<i>c</i> is the wave number. The sign chosen in the argument determines the direction of movement of the waves.</p> <p>Here is a plane wave moving on a three-dimensional lattice of atoms:</p> <div class="view"> <script> /* eslint-disable prefer-const*/ let parent = document.scripts[ document.scripts.length - 1 ].parentNode; parent.displacement = function ( x, y, z, t, target ) { return target.set( Math.sin( x - t ), 0, 0 ); }; parent.lattice = true; </script> </div> <p>Here is a plane wave moving through a three-dimensional random distribution of molecules:</p> <div class="view"> <script> parent = document.scripts[ document.scripts.length - 1 ].parentNode; parent.displacement = function ( x, y, z, t, target ) { return target.set( Math.sin( x - t ), 0, 0 ); }; parent.lattice = false; </script> </div> <p>Sound waves whose geometry is determined by two dimensions, cylindrical waves, obey the wave equation</p> <div class="math"> <span class="math-frac"> <span class="math-num"> ∂<sup>2</sup><i>u</i> </span> <span class="math-denom"> ∂<i>r</i><sup>2</sup> </span> </span> + <span class="math-frac"> <span class="math-num"> 1 </span> <span class="math-denom"> <i>r</i> </span> </span> <span class="math-frac"> <span class="math-num"> ∂<i>u</i> </span> <span class="math-denom"> ∂<i>r</i> </span> </span> − <span class="math-frac"> <span class="math-num"> 1<sup></sup> <!-- sup for vertical alignment --> </span> <span class="math-denom"> <i>c</i><sup>2</sup> </span> </span> <span class="math-frac"> <span class="math-num"> ∂<sup>2</sup><i>u</i> </span> <span class="math-denom"> ∂<i>t</i><sup>2</sup> </span> </span> = 0 </div> <p>The monochromatic solution for cylindrical sound waves will be taken to be</p> <div class="math"> <i>u</i>(<i>r</i>,<i>t</i>) = <span class="math-frac"> <span class="math-num"> sin(<i>k</i><i>r</i> ± ω<i>t</i>) </span> <span class="math-denom"> <span class="math-sqrt">√</span><span class="math-sqrt-stem"><i>r</i></span> </span> </span> </div> <p>Here is a cylindrical wave moving on a three-dimensional lattice of atoms:</p> <div class="view"> <script> parent = document.scripts[ document.scripts.length - 1 ].parentNode; parent.displacement = function ( x, y, z, t, target ) { if ( x * x + y * y < 0.01 ) { return target.set( 0, 0, 0 ); } else { const rho = Math.sqrt( x * x + y * y ); const phi = Math.atan2( y, x ); return target.set( 1.5 * Math.cos( phi ) * Math.sin( rho - t ) / Math.sqrt( rho ), 1.5 * Math.sin( phi ) * Math.sin( rho - t ) / Math.sqrt( rho ), 0 ); } }; parent.lattice = true; </script> </div> <p>Here is a cylindrical wave moving through a three-dimensional random distribution of molecules:</p> <div class="view"> <script> parent = document.scripts[ document.scripts.length - 1 ].parentNode; parent.displacement = function ( x, y, z, t, target ) { if ( x * x + y * y < 0.01 ) { return target.set( 0, 0, 0 ); } else { const rho = Math.sqrt( x * x + y * y ); const phi = Math.atan2( y, x ); return target.set( 1.5 * Math.cos( phi ) * Math.sin( rho - t ) / Math.sqrt( rho ), 1.5 * Math.sin( phi ) * Math.sin( rho - t ) / Math.sqrt( rho ), 0 ); } }; parent.lattice = false; </script> </div> <p>Sound waves whose geometry is determined by three dimensions, spherical waves, obey the wave equation</p> <div class="math"> <span class="math-frac"> <span class="math-num"> ∂<sup>2</sup><i>u</i> </span> <span class="math-denom"> ∂<i>r</i><sup>2</sup> </span> </span> + <span class="math-frac"> <span class="math-num"> 2 </span> <span class="math-denom"> <i>r</i> </span> </span> <span class="math-frac"> <span class="math-num"> ∂<i>u</i> </span> <span class="math-denom"> ∂<i>r</i> </span> </span> − <span class="math-frac"> <span class="math-num"> 1<sup></sup> <!-- sup for vertical alignment --> </span> <span class="math-denom"> <i>c</i><sup>2</sup> </span> </span> <span class="math-frac"> <span class="math-num"> ∂<sup>2</sup><i>u</i> </span> <span class="math-denom"> ∂<i>t</i><sup>2</sup> </span> </span> = 0 </div> <p>The monochromatic solution for spherical sound waves will be taken to be</p> <div class="math"> <i>u</i>(<i>r</i>,<i>t</i>) = <span class="math-frac"> <span class="math-num"> sin(<i>k</i><i>r</i> ± ω<i>t</i>) </span> <span class="math-denom"> <i>r</i> </span> </span> </div> <p>Here is a spherical wave moving on a three-dimensional lattice of atoms:</p> <div class="view"> <script> parent = document.scripts[ document.scripts.length - 1 ].parentNode; parent.displacement = function ( x, y, z, t, target ) { if ( x * x + y * y + z * z < 0.01 ) { return target.set( 0, 0, 0 ); } else { const r = Math.sqrt( x * x + y * y + z * z ); const theta = Math.acos( z / r ); const phi = Math.atan2( y, x ); return target.set( 3 * Math.cos( phi ) * Math.sin( theta ) * Math.sin( r - t ) / r, 3 * Math.sin( phi ) * Math.sin( theta ) * Math.sin( r - t ) / r, 3 * Math.cos( theta ) * Math.sin( r - t ) / r ); } }; parent.lattice = true; </script> </div> <p>Here is a spherical wave moving through a three-dimensional random distribution of molecules:</p> <div class="view"> <script> parent = document.scripts[ document.scripts.length - 1 ].parentNode; parent.displacement = function ( x, y, z, t, target ) { if ( x * x + y * y + z * z < 0.01 ) { return target.set( 0, 0, 0 ); } else { const r = Math.sqrt( x * x + y * y + z * z ); const theta = Math.acos( z / r ); const phi = Math.atan2( y, x ); return target.set( 3 * Math.cos( phi ) * Math.sin( theta ) * Math.sin( r - t ) / r, 3 * Math.sin( phi ) * Math.sin( theta ) * Math.sin( r - t ) / r, 3 * Math.cos( theta ) * Math.sin( r - t ) / r ); } }; parent.lattice = false; </script> </div> <p>The mathematical description of sound waves can be carried to higher dimensions, but one needs to wait for Four.js and its higher-dimensional successors to attempt visualizations.</p> </body> </html>
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