P 1 (0,0) will be considered starting pointsįollowing Figure show line plotted using these points. How many different points will be generated? In the case of the symmetrical DDA, we choose ε=2 -n,where 2 n-1≤max (|∆x|,|∆y|)<2 πĪ line drawn with the symmetrical DDA is shown in fig:Įxample: If a line is drawn from (0, 0) to (10, 5) with a symmetrical DDAĢ. The integer parts of the x and y registers are used in plotting the line. The incrementing values, which are both less than unity, are repeatedly added to the fractional parts and whenever the results overflows, the corresponding integer part is incremented. An alternative to rounding the use of arithmetic overflow: x and y are kept in registers that have two parts, integer and fractional. By rounding to the nearest integer after each incremental step, after rounding we display dots at the resultant x and y.Ģ. Therefore, we could generate a line by incrementing x and y by ϵ ∆x and ϵ ∆y, where ϵ is some small quantity. The following example shows how to use this method to get the angle between two Vector structures. In this case of a straight line, the first derivatives are constant and are proportional to ∆x and ∆y. The angle, in degrees, between vector1 and vector2. The DDA works on the principle that we simultaneously increment x and y by small steps proportional to the first derivatives of x and y. When calculating values of these, it is important to realize that the angle can be measured in various ways, the most common being. Here cos is the cosine function and sin is the sine function. The Digital Differential Analyzer (DDA) generates lines from their differential equations. In general, if is the angle between the line of sight from the entity to the point and the positive x axis, then. Program to implement DDA Line Drawing Algorithm: How many points will needed to generate such line?įor calculating next value of x takes x = x + Y i+1-x i=∆x.equation 4Įxample: If a line is drawn from (2, 3) to (6, 15) with use of DDA. Suppose at step i, the pixels is (x i,y i) In this method calculation is performed at each step but by using results of previous steps. It is an incremental method of scan conversion of line. Move point B and you will see that the perp is always the same with the x and y swapped and one negated.DDA stands for Digital Differential Analyzer. The perpendicular ( aka normal )can be found by simply swapping the x and y values and negating one of the two -> ĭepending on which on you negate gives you the directing your vector goes into.Įdit: Geogebra can easily visualize this. Note: if two vectors are parallel the resulting vector will be. Provided that both vectors are normalized. The c vector is your perpendicular vector to the plane. Shift the x component to the bottom, multiply each component with their diagonal and subtract The cross product can be calculated very quick by applying the following trick: If GLM doesn't have the cross product function you can simply do it manually: Your fingers represent the vectors, that's your plane. Visualize this by making a right angle between your thumb and index finger. To get the perpendicular of a plane you simply need 2 vectors and take the cross product of the two. So the question was for 3D and It isn't very clear whether you're drawing 2 vectors or 3. Apply it to the point in space we are rotating around To_return = glm::rotate(to_return, angle* RAD_TO_DEG, normal) Glm::vec3 to_return = glm::normalize(glm::cross(normal,to_cross)) If we define pitch0 as horizontal (z0) and yaw as counter-clockwise from the x axis, then the direction vector will be x cos (yaw)cos (pitch) y sin (yaw)cos (pitch) z sin (pitch) Note that I haven't used roll this is direction unit vector, it doesn't specify attitude. Make sure that the normal and cross vector are not the same, if they are change the cross vector Create a vector that will be used for the dot product Normalize the normal (axis to rotate on) Solution Code glm::vec3 CreateAngledPoint(glm::vec3 rotation_point, float radius, float angle, glm::vec3 normal) The reason for this is so I can loop through and create a point cloud in 3D space and then join them together to make shapes such as cylinders (see photo) The function's purpose is to pass a direction vector into a function, radius, and an angle and it will create a point around the origin at x angle in space. Here is a basic visualization of what I need. I would like to keep the solution compatible with GLM as I wish to have everything standardized. I have been using GLM and have tried using its built in vector rotation functions but to no avail. I understand that in 3D there is an infinite amount of vectors that could be produced from this calculation, but I only require 1. I need a function that can take a vector as an input and provide a vector that is at a 90-degree angle to the provided vector.
0 Comments
Leave a Reply. |