Collision Detection and Resolution in Virtual Environments

A computer-implemented method for collision prediction comprising:

• determining a first representative point, wherein the first representative point represents a first geometric primitive;
• determining a second representative point, wherein the second representative point represents a second geometric primitive;
• determining an initial distance between the first representative point and the second representative point;
• calculating a first displacement based on a velocity of the first representative point;
• calculating a second displacement based on a velocity of the second representative point;
• determining a separating direction between the first representative point and the second representative point;
• projecting the first displacement along the separating direction;
• projecting the second displacement along the separating direction;
• calculating a predicted minimum distance between the first representative point and the second representative point based on the projection of the first displacement along the separating direction, the projection of the second displacement along the separating direction and the initial distance between the first representative point and the second representative point;
• and
• in response to the predicted minimum distance being less than a threshold distance, generating a collision constraint preventing penetration between the first geometric primitive and the second geometric primitive.

An apparatus comprising:

• at least one processor;
• and
• at least one memory including computer program code which, when executed by the at least one processor, cause the apparatus to:
• determine a first representative point, wherein the first representative point represents a first geometric primitive;
• determine a second representative point, wherein the second representative point represents a second geometric primitive;
• determine an initial distance between the first representative point and the second representative point;
• calculate a first displacement based on a velocity of the first representative point;
• calculate a second displacement based on a velocity of the second representative point;
• determine a separating direction between the first representative point and the second representative point;
• project the first displacement along the separating direction;
• project the second displacement along the separating direction;
• calculate a predicted minimum distance between the first representative point and the second representative point based on the projection of the first displacement along the separating direction, the projection of the second displacement along the separating direction and the initial distance between the first representative point and the second representative point;
• and
• in response to the predicted minimum distance being less than a threshold distance, generate a collision constraint preventing penetration between the first geometric primitive and the second geometric primitive.