Distance determination for mixed reality interaction

A system comprising:

• a processor;
• and
• a memory storing instructions that, when executed by the processor, configure the system to perform operations comprising:
• determining, by one or more processors, a first position of a point of a surface based on a distance from a right camera and a left camera of a mobile device being equal to:
• (R*X0)/(2*tan((Θ1/2)+C)*(x2−x1)), where R is a distance between an optical axis of the left camera and an optical axis of the right camera, X0 is a width of the point in pixels of an image sensor of the left camera, x2 is a number of pixels from the optical axis of an image sensor of the right camera, x1 is a number of pixels from the optical axis of the left camera, Θ1 is a view angle of the left camera and the right camera, and C is a compensation for distortions of the mobile device;
• rendering on a display, of the mobile device of a user, a virtual reality (VR) interactive item comprising a VR interactive control, wherein the VR interactive item and the VR interactive control are rendered to appear to the user to be on the surface at the first position of the surface;
• tracking a control indicator controlled by the user by determining a first plurality of positions of the control indicator;
• activating the VR interactive control in response to detecting the control indicator controlled by the user transgressing a first threshold distance from the VR interactive control;
• determining a closest position of the first plurality of positions to the point based on the first position;
• determining the point of the surface to have a second position based on the determined closest position plus a constant for the control indicator;
• and
• associating a second threshold distance, less than the first threshold distance, with the point of the surface.

A non-transitory computer-readable storage medium, the computer-readable storage medium including instructions that when executed by a computer, cause the computer to perform operations comprising:

• determining, by one or more processors, a first position of a point of a surface based on a distance from a right camera and a left camera of a mobile device being equal to:
• (R*X0)/(2*tan((Θ1/2)+C)*(x2−x1)), where R is a distance between an optical axis of the left camera and an optical axis of the right camera, X0 is a width of the point in pixels of an image sensor of the left camera, x2 is a number of pixels from the optical axis of an image sensor of the right camera, x1 is a number of pixels from the optical axis of the left camera, Θ1 is a view angle of the left camera and the right camera, and C is a compensation for distortions of the mobile device;
• rendering on a display, of the mobile device of a user, a virtual reality (VR) interactive item comprising a VR interactive control, wherein the VR interactive item and the VR interactive control are rendered to appear to the user to be on the surface at the first position of the surface;
• tracking a control indicator controlled by the user by determining a first plurality of positions of the control indicator;
• activating the VR interactive control in response to detecting the control indicator controlled by the user transgressing a first threshold distance from the VR interactive control;
• determining a closest position of the first plurality of positions to the point based on the first position;
• determining the point of the surface to have a second position based on the determined closest position plus a constant for the control indicator;
• and
• associating a second threshold distance, less than the first threshold distance, with the point of the surface.