Abstract: Methods and apparatus are provided for displaying shadows of circular light sources. A computing device can determine a light source and an occluding polygon that is between the light source and a receiver surface, where the occluding polygon includes vertices connected by edges. The computing device can determine a shadow of the occluding polygon on the receiver surface by at least: determining, for a particular vertex, a projection vertex on the receiver surface by projecting a ray from the center point through the particular vertex; determining an outline polygon based on the projection vertex; determining a projection circle around the projection vertex; determining a penumbra of the shadow based on exterior tangents outside of the outline polygon; and determining an umbra of the shadow based on interior tangents inside the outline polygon. The computing device can display at least part of the shadow.

Abstract: Methods and apparatus are provided for displaying shadows of circular light sources. A computing device can determine a light source and an occluding polygon that is between the light source and a receiver surface, where the occluding polygon includes vertices connected by edges. The computing device can determine a shadow of the occluding polygon on the receiver surface by at least: determining, for a particular vertex, a projection vertex on the receiver surface by projecting a ray from the center point through the particular vertex; determining an outline polygon based on the projection vertex; determining a projection circle around the projection vertex; determining a penumbra of the shadow based on exterior tangents outside of the outline polygon; and determining an umbra of the shadow based on interior tangents inside the outline polygon. The computing device can display at least part of the shadow.

Abstract: Methods and apparatus are provided for displaying shadows of circular light sources. A computing device can determine a light source and an occluding polygon that is between the light source and a receiver surface, where the occluding polygon includes vertices connected by edges. The computing device can determine a shadow of the occluding polygon on the receiver surface by at least: determining, for a particular vertex, a projection vertex on the receiver surface by projecting a ray from the center point through the particular vertex; determining an outline polygon based on the projection vertex; determining a projection circle around the projection vertex; determining a penumbra of the shadow based on exterior tangents outside of the outline polygon; and determining an umbra of the shadow based on interior tangents inside the outline polygon. The computing device can display at least part of the shadow.

Abstract: Methods and apparatus are provided for displaying shadows of circular light sources. A computing device can determine a light source and an occluding polygon that is between the light source and a receiver surface, where the occluding polygon includes vertices connected by edges. The computing device can determine a shadow of the occluding polygon on the receiver surface by at least: determining, for a particular vertex, a projection vertex on the receiver surface by projecting a ray from the center point through the particular vertex; determining an outline polygon based on the projection vertex; determining a projection circle around the projection vertex; determining a penumbra of the shadow based on exterior tangents outside of the outline polygon; and determining an umbra of the shadow based on interior tangents inside the outline polygon. The computing device can display at least part of the shadow.

Abstract: Methods and apparatus are provided for displaying shadows of polygonal light sources. A computing device can determine a light-source polygon of a polygonal light source, where the light-source polygon includes light-source vertices. The computing device can determine an occluding polygon between the light-source polygon and a background surface. The computing device can determine a shadow of the occluding polygon on the background surface by: for each light-source vertex, determining a vertex-shadow region of the background surface corresponding to a shadow cast upon the background surface by the occluding polygon for light emitted from the light-source vertex, determining an umbra of the shadow based on an intersection of the vertex-shadow regions, and determining a penumbra of the shadow based on a convex representation of a union of vertex-shadow regions. The computing device can display the shadow.

Abstract: Methods and apparatus are provided for displaying shadows of polygonal light sources. A computing device can determine a light-source polygon of a polygonal light source, where the light-source polygon includes light-source vertices. The computing device can determine an occluding polygon between the light-source polygon and a background surface. The computing device can determine a shadow of the occluding polygon on the background surface by: for each light-source vertex, determining a vertex-shadow region of the background surface corresponding to a shadow cast upon the background surface by the occluding polygon for light emitted from the light-source vertex, determining an umbra of the shadow based on an intersection of the vertex-shadow regions, and determining a penumbra of the shadow based on a convex representation of a union of vertex-shadow regions. The computing device can display the shadow.