Engineering

Proof that the vector from the viewpoint of a pinhole camera to the vanishing point (in the image plane) of a set of 3D parallel lines is parallel to the direction of the parallel lines:Let L be a set of parallel 3D lines, and let v be their vanishing point in the image plane. Let O be the viewpoint of the camera. We want to prove that the vector from O to v is parallel to the direction of the lines in L.Consider two lines l1 and l2 in L. Let P1 and P2 be two points on these lines. Let IP1 and IP2 be the interpretation planes of these lines passing through O. Since the lines are parallel, the interpretation planes are also parallel. Let l be the line of intersection of the interpretation planes, passing through O. Let Q1 and Q2 be the projections of P1 and P2 onto the image plane, respectively. Let v be the vanishing point of the lines in L. Then, Q1Q2 is parallel to the lines in L and passes through v. Let R1 and R2 be the intersections of IP1 and IP2 with the image plane, respectively. Then, R1R2 is parallel to Q1Q2 and passes through O. By the similar triangles formed by the image plane, the interpretation plane, and the object plane, we have:|OR1|/|OQ1| = |OR2|/|OQ2|.Since R1R2 is parallel to the lines in L, and Q1Q2 is parallel to the image plane, we have:|OR1|/|OQ1| = |R1R2|/|Q1Q2|.Therefore, |R1R2|/|Q1Q2| = |OR2|/|OQ2|.Since Q1Q2 is parallel to L, and R1R2 is the intersection of the image plane and the interpretation planes of l1 and l2, we have: |R1R2|/|Q1Q2| = |P1P2|/|L|,where |L| is the length of the segment between P1 and P2 on the lines in L.Therefore, |P1P2|/|L| = |OR2|/|OQ2|.Since this equation holds for any two points P1 and P2 on the lines in L, we conclude that the vector from O to v is parallel to the direction of the lines in L.
Find solutions for your homeworkengineeringcomputer sciencecomputer science questions and answersquestion 14 1 points save answer match the name of the approach towards implementing a control plane with a description of how this approach works. v per-router control plane. a. a typically) remote controller computes and installs forwarding tables in routers. ? software-defined networking (sdn). b. an individual routing algorithm components in each andQuestion:Question 14 1 Points Save Answer Match The Name Of The Approach Towards Implementing A Control Plane With A Description Of How This Approach Works. V Per-Router Control Plane. A. A Typically) Remote Controller Computes And Installs Forwarding Tables In Routers. ? Software-Defined Networking (SDN). B. An Individual Routing Algorithm Components In Each AndShow transcribed image textExpert Answer1st stepAll stepsFinal answerStep 1/1Two functions of the network layer are forwarding and routing.Packet forwarding - It includes forwarding packets that enter the router to the appropriate router output.Packet routing - Packet routing involves the process of determining the route taken by packets to reach their destination.View the full answerFinal answerTranscribed image text:Question 14 1 points Save Answer Match the name of the approach towards implementing a control plane with a description of how this approach works. v Per-router control plane. A. A typically) remote controller computes and installs forwarding tables in routers. ? Software-defined networking (SDN). B. An individual routing algorithm components in each and every router interact in the control plane C. The network operator installs forwarding tables using the Simple Network Management Protocols (SNMP).