36. Perspective Drawing: Where are Measuring Points

How to find measuring points when the vanishing point is off the page.

[@user-sz1gn4pu8g]

Mathematically LMP (left measurement point) can be found with help from trigonometry. You will find that LMP's distance from CV (center of vision) on the horizontal line will depend on the degree that LVP (left vanishing point) and CV form to the SP (station point) and the length between CV to SP. If we generalize the variables we can make a formula that will always be able to calculate the distance on any MP (measurement point) so lets label them.The angle (either degrees or radians will do) that a VP (vanishing point) and CV form to SP we will call "α" (alpha), the distance (in preferred unit) between CV and SP we will call "R", and finally the distance between CV and MP on the horizon line we will call "L". L = ( R * ( ( 1 / ( cos (α) ) ) - ( tan (α) ) ) ) Note that L's unit will depend on which unit you used between CV and SP and it is important to use the right setting between degrees and radians on the calculator depending on which you used because the relationship between a right triangles sides and the sine functions for the angle differ depending on which unit is used. I hope this will be of any use ;)

[@trustyourperspective]

Kudos! Good job. Yes, It's all math. There's always several solutions for perspective problems. Yours is impressive. But, I'm doing these for artists who are not widely known for their mathematical prowess. So if you are an artist out there, you can use: L = ( R * ( ( 1 / ( cos (α) ) ) - ( tan (α) ) ) ). The other option would be to use a compass. I suppose you can toss a coin to decide🤔