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Intersecting Segments (In Space).
Distance Between Two Points.
Line In Space (Two Point Method).
Line In Space (Direction Angle Method).
Direction Angles Of An Axis.
Parallel Movement Transformation.
Rotation Of A Point About A Axis.
The Distance Between Two Points Is A Straight Line.
m1 Is The Distance Point3 Moves From Point1 Towards Point2.
Direction Angles Of A Segment.
alpha1, beta1, gamma1, Are The Direction Angles In (radians).
An Axis Is A Line That Intersects The Center Of The Coordinate System.
m1 Is The Distance Point3 Moves From Point1 In The Direction Towards Point2.
Parallel Movement Transformation Can Move A Set Of Points In The Same Direction And At The Same Distance.
Rotation Of A Point About A Axis. Theta Is The Rotation Angle In (radians). Alpha, Beta, Gamma Are The Direction Angles Of The Axis In (radians). Point4 Is The (Point) To Be Rotated. Point5 Is Point4 After Rotation Is Applied.
Rotation About The X Axis.
Rotates Point4 About The Coordinate System X Axis.
Rotation About The Y Axis.
Rotates Point4 About The Coordinate System Y Axis.
Rotation About The Z Axis.
Rotates Point4 About The Coordinate System Z Axis.
Perpendicular Segment Of A Segment Using A Right Angle Rotation About The X Axis And Parallel Movement Transformation.
Perpendicular Segment Of A Segment Using A Right Angle Rotation About The Y Axis And Parallel Movement Transformation.
Perpendicular Segment Of A Segment Using A Right Angle Rotation About The Z Axis And Parallel Movement Transformation.
If y1 = y2 && z1 = z2: Choose Rotation About The Y Axis Or Rotation About The Z Axis.
If x1 = x2 && z1 = z2: Choose Rotation About The X Axis Or Rotation About The Z Axis.
If x1 = x2 && y1 = y2: Choose Rotation About The X Axis Or Rotation About The Y Axis.
Intersecting Segments. (In Plane).
Point5 Is The Intersection Point.
Point5 Is The Intersection Point.
Point1 {x1,y1} Is The Circle's Center, r1 Is The Circle's Radius, theta1 Is The Rotation Angle In (radians) That Point3 Travels About The Center Tethered To Point1 By The Radius. One Complete Rotation Is 2 (radians).
Perpendicular (Artificial Plane) Intersecting A Point On A Line Using Rotation About The X Axis And Rotation About The Y Axis And Parallel Movement Transformation.
m1 is the Distance From Point1 Towards Point2, Point3 Is The Perpendicular Artifical Planes Intersection Point On The Line. Point4 Is The Planes Perpendicular Plot Using xx1, yy1 values.
y[1] y[2] &&
z[1] z[2]
x[1] x[2] &&
z[1] z[2]
Perpendicular (Artificial Plane) Intersecting A Point On A Line Using Rotation About The Y Axis And Rotation About The Z Axis And Parallel Movement Transformation.
x[1] x[2] &&
z[1] z[2]
x[1] x[2] &&
y[1] y[2]
m1 is the Distance From Point1 Towards Point2, Point3 Is The Perpendicular Artifical Planes Intersection Point On The Line. Point4 Is The Planes Perpendicular Plot Using xx1, yy1 values.
Perpendicular (Artificial Plane) Intersecting A Point On A Line Using Rotation About The Z Axis And Rotation About The X Axis. And Parallel Movement Transformation.
x[1] x[2] &&
y[1] y[2]
y[1] y[2] &&
z[1] z[2]
m1 is the Distance From Point1 Towards Point2, Point3 Is The Perpendicular Artifical Planes Intersection Point On The Line. Point4 Is The Planes Perpendicular Plot Using xx1, yy1 values.
A Parabola Is A Curve That Reflects Light From A Extremely Far Source (Straight Down) Into A Focal Point.
f1 is the focal point Located At {x1=0,y1=f1}
A Ellipse Is A Curve That Reflects Light From A Focal Point f1 {-c1,0} Into Another Focal Point f2 {c1,0}. And Visa Versa.
An Ellipse Can Be Plotted As A Complex Circle. Based On A Center Point {x0,y0}, theta1 Is The Rotation Angle In (radians).