Geo. Geo.
This library provides a comprehensive set of geometric functions based on 2 simple types for point and line manipulation, point array calculations, some vector operations (Borrowed from @ricardosantos ), angle calculations, and basic polygon analysis. It offers tools for creating, transforming, and analyzing geometric shapes and their relationships.
View the source code for detailed documentation on each function and type.
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█ OVERVIEW
This library enhances TradingView's Pine Script with robust geometric capabilities. It introduces the Point and Line types, along with a suite of functions for various geometric operations. These functionalities empower you to perform advanced calculations, manipulations, and analyses involving points, lines, vectors, angles, and polygons directly within your Pine scripts. The example is at the bottom of the script. ( Commented out )
█ CONCEPTS
This library revolves around two fundamental types:
• Point: Represents a point in 2D space with x and y coordinates, along with optional 'a' (angle) and 'v' (value) fields for versatile use. Crucially, for plotting, utilize the `.to_chart_point()` method to convert Points into plottable chart.point objects.
• Line: Defined by a starting Point and a slope , enabling calculations like getting y for a given x, or finding intersection points.
█ FEATURES
• Point Manipulation: Perform operations like addition, subtraction, scaling, rotation, normalization, calculating distances, dot products, cross products, midpoints, and more with Point objects.
• Line Operations: Create lines, determine their slope, calculate y from x (and vice versa), and find the intersection points of two lines.
• Vector Operations: Perform vector addition, subtraction, multiplication, division, negation, perpendicular vector calculation, floor, fractional part, sine, absolute value, modulus, sign, round, scaling, rescaling, rotation, and ceiling operations.
• Angle Calculations: Compute angles between points in degrees or radians, including signed, unsigned, and 360-degree angles.
• Polygon Analysis: Calculate the area, perimeter, and centroid of polygons. Check if a point is inside a given polygon and determine the convex hull perimeter.
• Chart Plotting: Conveniently convert Point objects to chart.point objects for plotting lines and points on the chart. The library also includes functions for plotting lines between individual and series of points.
• Utility Functions: Includes helper functions such as square root, square, cosine, sine, tangent, arc cosine, arc sine, arc tangent, atan2, absolute distance, golden ratio tolerance check, fractional part, and safe index/check for chart plotting boundaries.
█ HOW TO USE
1 — Include the library in your script using:
import kaigouthro/geo/1
2 — Create Point and Line objects:
p1 = geo.Point(bar_index, close)
p2 = geo.Point(bar_index , open)
myLine = geo.Line(p1, geo.slope(p1, p2))
// maybe use that line to detect a crossing for an alert ... hmmm
3 — Utilize the provided functions:
distance = geo.distance(p1, p2)
intersection = geo.intersection(line1, line2)
4 — For plotting labels, lines, convert Point to chart.point :
label.new(p1.to_chart_point(), " Hi ")
line.new(p1.to_chart_point(),p2.to_chart_point())
█ NOTES
This description provides a concise overview. Consult the library's source code for in-depth documentation, including detailed descriptions, parameter types, and return values for each function and method. The source code is structured with comprehensive comments using the `//@` format for seamless integration with TradingView's auto-documentation features.
█ Possibilities..
Library "geo"
This library provides a comprehensive set of geometric functions and types, including point and line manipulation, vector operations, angle calculations, and polygon analysis. It offers tools for creating, transforming, and analyzing geometric shapes and their relationships.
sqrt(value)
Square root function
Parameters:
value (float) : (float) - The number to take the square root of
Returns: (float) - The square root of the input value
sqr(x)
Square function
Parameters:
x (float) : (float) - The number to square
Returns: (float) - The square of the input value
cos(v)
Cosine function
Parameters:
v (float) : (series float) - The value to find the cosine of
Returns: (series float) - The cosine of the input value
sin(v)
Sine function
Parameters:
v (float) : (series float) - The value to find the sine of
Returns: (series float) - The sine of the input value
tan(v)
Tangent function
Parameters:
v (float) : (series float) - The value to find the tangent of
Returns: (series float) - The tangent of the input value
acos(v)
Arc cosine function
Parameters:
v (float) : (series float) - The value to find the arc cosine of
Returns: (series float) - The arc cosine of the input value
asin(v)
Arc sine function
Parameters:
v (float) : (series float) - The value to find the arc sine of
Returns: (series float) - The arc sine of the input value
atan(v)
Arc tangent function
Parameters:
v (float) : (series float) - The value to find the arc tangent of
Returns: (series float) - The arc tangent of the input value
atan2(dy, dx)
atan2 function
Parameters:
dy (float) : (float) - The y-coordinate
dx (float) : (float) - The x-coordinate
Returns: (float) - The angle in radians
gap(_value1, __value2)
Absolute distance between any two float values
Parameters:
_value1 (float) : First value
__value2 (float)
Returns: Absolute Positive Distance
phi_tol(a, b, tolerance)
Check if the ratio is within the tolerance of the golden ratio
Parameters:
a (float) : (float) The first number
b (float) : (float) The second number
tolerance (float) : (float) The tolerance percennt as 1 = 1 percent
Returns: (bool) True if the ratio is within the tolerance, false otherwise
frac(x)
frad Fractional
Parameters:
x (float) : (float) - The number to convert to fractional
Returns: (float) - The number converted to fractional
safeindex(x, limit)
limiting int to hold the value within the chart range
Parameters:
x (float) : (float) - The number to limit
limit (int)
Returns: (int) - The number limited to the chart range
safecheck(x, limit)
limiting int check if within the chartplottable range
Parameters:
x (float) : (float) - The number to limit
limit (int)
Returns: (int) - The number limited to the chart range
interpolate(a, b, t)
interpolate between two values
Parameters:
a (float) : (float) - The first value
b (float) : (float) - The second value
t (float) : (float) - The interpolation factor (0 to 1)
Returns: (float) - The interpolated value
gcd(_numerator, _denominator)
Greatest common divisor of two integers
Parameters:
_numerator (int)
_denominator (int)
Returns: (int) The greatest common divisor
method set_x(self, value)
Set the x value of the point, and pass point for chaining
Namespace types: Point
Parameters:
self (Point) : (Point) The point to modify
value (float) : (float) The new x-coordinate
method set_y(self, value)
Set the y value of the point, and pass point for chaining
Namespace types: Point
Parameters:
self (Point) : (Point) The point to modify
value (float) : (float) The new y-coordinate
method get_x(self)
Get the x value of the point
Namespace types: Point
Parameters:
self (Point) : (Point) The point to get the x-coordinate from
Returns: (float) The x-coordinate
method get_y(self)
Get the y value of the point
Namespace types: Point
Parameters:
self (Point) : (Point) The point to get the y-coordinate from
Returns: (float) The y-coordinate
method vmin(self)
Lowest element of the point
Namespace types: Point
Parameters:
self (Point) : (Point) The point
Returns: (float) The lowest value between x and y
method vmax(self)
Highest element of the point
Namespace types: Point
Parameters:
self (Point) : (Point) The point
Returns: (float) The highest value between x and y
method add(p1, p2)
Addition
Namespace types: Point
Parameters:
p1 (Point) : (Point) - The first point
p2 (Point) : (Point) - The second point
Returns: (Point) - the add of the two points
method sub(p1, p2)
Subtraction
Namespace types: Point
Parameters:
p1 (Point) : (Point) - The first point
p2 (Point) : (Point) - The second point
Returns: (Point) - the sub of the two points
method mul(p, scalar)
Multiplication by scalar
Namespace types: Point
Parameters:
p (Point) : (Point) - The point
scalar (float) : (float) - The scalar to multiply by
Returns: (Point) - the multiplied point of the point and the scalar
method div(p, scalar)
Division by scalar
Namespace types: Point
Parameters:
p (Point) : (Point) - The point
scalar (float) : (float) - The scalar to divide by
Returns: (Point) - the divided point of the point and the scalar
method rotate(p, angle)
Rotate a point around the origin by an angle (in degrees)
Namespace types: Point
Parameters:
p (Point) : (Point) - The point to rotate
angle (float) : (float) - The angle to rotate by in degrees
Returns: (Point) - the rotated point
method length(p)
Length of the vector from origin to the point
Namespace types: Point
Parameters:
p (Point) : (Point) - The point
Returns: (float) - the length of the point
method length_squared(p)
Length squared of the vector
Namespace types: Point
Parameters:
p (Point) : (Point) The point
Returns: (float) The squared length of the point
method normalize(p)
Normalize the point to a unit vector
Namespace types: Point
Parameters:
p (Point) : (Point) - The point to normalize
Returns: (Point) - the normalized point
method dot(p1, p2)
Dot product
Namespace types: Point
Parameters:
p1 (Point) : (Point) - The first point
p2 (Point) : (Point) - The second point
Returns: (float) - the dot of the two points
method cross(p1, p2)
Cross product result (in 2D, this is a scalar)
Namespace types: Point
Parameters:
p1 (Point) : (Point) - The first point
p2 (Point) : (Point) - The second point
Returns: (float) - the cross of the two points
method distance(p1, p2)
Distance between two points
Namespace types: Point
Parameters:
p1 (Point) : (Point) - The first point
p2 (Point) : (Point) - The second point
Returns: (float) - the distance of the two points
method Point(x, y, a, v)
Point Create Convenience
Namespace types: series float, simple float, input float, const float
Parameters:
x (float)
y (float)
a (float)
v (float)
Returns: (Point) new point
method angle(p1, p2)
Angle between two points in degrees
Namespace types: Point
Parameters:
p1 (Point) : (Point) - The first point
p2 (Point) : (Point) - The second point
Returns: (float) - the angle of the first point and the second point
method angle_between(p, pivot, other)
Angle between two points in degrees from a pivot point
Namespace types: Point
Parameters:
p (Point) : (Point) - The point to calculate the angle from
pivot (Point) : (Point) - The pivot point
other (Point) : (Point) - The other point
Returns: (float) - the angle between the two points
method translate(p, from_origin, to_origin)
Translate a point from one origin to another
Namespace types: Point
Parameters:
p (Point) : (Point) - The point to translate
from_origin (Point) : (Point) - The origin to translate from
to_origin (Point) : (Point) - The origin to translate to
Returns: (Point) - the translated point
method midpoint(p1, p2)
Midpoint of two points
Namespace types: Point
Parameters:
p1 (Point) : (Point) - The first point
p2 (Point) : (Point) - The second point
Returns: (Point) - The midpoint of the two points
method rotate_around(p, angle, pivot)
Rotate a point around a pivot point by an angle (in degrees)
Namespace types: Point
Parameters:
p (Point) : (Point) - The point to rotate
angle (float) : (float) - The angle to rotate by in degrees
pivot (Point) : (Point) - The pivot point to rotate around
Returns: (Point) - the rotated point
method multiply(_a, _b)
Multiply vector _a with _b
Namespace types: Point
Parameters:
_a (Point) : (Point) The first point
_b (Point) : (Point) The second point
Returns: (Point) The result of the multiplication
method divide(_a, _b)
Divide vector _a by _b
Namespace types: Point
Parameters:
_a (Point) : (Point) The first point
_b (Point) : (Point) The second point
Returns: (Point) The result of the division
method negate(_a)
Negative of vector _a
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to negate
Returns: (Point) The negated point
method perp(_a)
Perpendicular Vector of _a
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
Returns: (Point) The perpendicular point
method vfloor(_a)
Compute the floor of argument vector _a
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
Returns: (Point) The floor of the point
method fractional(_a)
Compute the fractional part of the elements from vector _a
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
Returns: (Point) The fractional part of the point
method vsin(_a)
Compute the sine of argument vector _a
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
Returns: (Point) The sine of the point
lcm(a, b)
Least common multiple of two integers
Parameters:
a (int) : (int) The first integer
b (int) : (int) The second integer
Returns: (int) The least common multiple
method vabs(_a)
Compute the absolute of argument vector _a
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
Returns: (Point) The absolute of the point
method vmod(_a, _b)
Compute the mod of argument vector _a
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
_b (float) : (float) The mod
Returns: (Point) The mod of the point
method vsign(_a)
Compute the sign of argument vector _a
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
Returns: (Point) The sign of the point
method vround(_a)
Compute the round of argument vector _a
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
Returns: (Point) The round of the point
method normalize_y(p, height)
normalizes the y value of a point to an input height
Namespace types: Point
Parameters:
p (Point) : (Point) - The point to normalize
height (float) : (float) - The height to normalize to
Returns: (Point) - the normalized point
centroid(points)
Calculate the centroid of multiple points
Parameters:
points (array) : (array) The array of points
Returns: (Point) The centroid point
random_point(_height, _width, _origin, _centered)
Random Point in a given height and width
Parameters:
_height (float) : (float) The height of the area to generate the point in
_width (float) : (float) The width of the area to generate the point in
_origin (Point) : (Point) The origin of the area to generate the point in (default: na, will create a Point(0, 0))
_centered (bool) : (bool) Center the origin point in the area, otherwise, positive h/w (default: false)
Returns: (Point) The random point in the given area
random_point_array(_origin, _height, _width, _centered, _count)
Random Point Array in a given height and width
Parameters:
_origin (Point) : (Point) The origin of the area to generate the array (default: na, will create a Point(0, 0))
_height (float) : (float) The height of the area to generate the array
_width (float) : (float) The width of the area to generate the array
_centered (bool) : (bool) Center the origin point in the area, otherwise, positive h/w (default: false)
_count (int) : (int) The number of points to generate (default: 50)
Returns: (array) The random point array in the given area
method sort_points(points, by_x)
Sorts an array of points by x or y coordinate
Namespace types: array
Parameters:
points (array) : (array) The array of points to sort
by_x (bool) : (bool) Whether to sort by x-coordinate (true) or y-coordinate (false)
Returns: (array) The sorted array of points
method equals(_a, _b)
Compares two points for equality
Namespace types: Point
Parameters:
_a (Point) : (Point) The first point
_b (Point) : (Point) The second point
Returns: (bool) True if the points are equal, false otherwise
method max(origin, _a, _b)
Maximum of two points from origin, using dot product
Namespace types: Point
Parameters:
origin (Point)
_a (Point) : (Point) The first point
_b (Point) : (Point) The second point
Returns: (Point) The maximum point
method min(origin, _a, _b)
Minimum of two points from origin, using dot product
Namespace types: Point
Parameters:
origin (Point)
_a (Point) : (Point) The first point
_b (Point) : (Point) The second point
Returns: (Point) The minimum point
method avg_x(points)
Average x of point array
Namespace types: array
Parameters:
points (array) : (array) The array of points
Returns: (float) The average x-coordinate
method avg_y(points)
Average y of point array
Namespace types: array
Parameters:
points (array) : (array) The array of points
Returns: (float) The average y-coordinate
method range_x(points)
Range of x values in point array
Namespace types: array
Parameters:
points (array) : (array) The array of points
Returns: (float) The range of x-coordinates
method range_y(points)
Range of y values in point array
Namespace types: array
Parameters:
points (array) : (array) The array of points
Returns: (float) The range of y-coordinates
method max_x(points)
max of x values in point array
Namespace types: array
Parameters:
points (array) : (array) The array of points
Returns: (float) The max of x-coordinates
method min_y(points)
min of x values in point array
Namespace types: array
Parameters:
points (array) : (array) The array of points
Returns: (float) The min of x-coordinates
method scale(_a, _scalar)
Scale a point by a scalar
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to scale
_scalar (float) : (float) The scalar value
Returns: (Point) The scaled point
method rescale(_a, _length)
Rescale a point to a new magnitude
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to rescale
_length (float) : (float) The new magnitude
Returns: (Point) The rescaled point
method rotate_rad(_a, _radians)
Rotate a point by an angle in radians
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to rotate
_radians (float) : (float) The angle in radians
Returns: (Point) The rotated point
method rotate_degree(_a, _degree)
Rotate a point by an angle in degrees
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to rotate
_degree (float) : (float) The angle in degrees
Returns: (Point) The rotated point
method vceil(_a, _digits)
Ceil a point to a certain number of digits
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to ceil
_digits (int) : (int) The number of digits to ceil to
Returns: (Point) The ceiled point
method vpow(_a, _exponent)
Raise both point elements to a power
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
_exponent (float) : (float) The exponent
Returns: (Point) The point with elements raised to the power
method perpendicular_distance(_a, _b, _c)
Distance from point _a to line between _b and _c
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
_b (Point) : (Point) The start point of the line
_c (Point) : (Point) The end point of the line
Returns: (float) The perpendicular distance
method project(_a, _axis)
Project a point onto another
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to project
_axis (Point) : (Point) The point to project onto
Returns: (Point) The projected point
method projectN(_a, _axis)
Project a point onto a point of unit length
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to project
_axis (Point) : (Point) The unit length point to project onto
Returns: (Point) The projected point
method reflect(_a, _axis)
Reflect a point on another
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to reflect
_axis (Point) : (Point) The point to reflect on
Returns: (Point) The reflected point
method reflectN(_a, _axis)
Reflect a point to an arbitrary axis
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to reflect
_axis (Point) : (Point) The axis to reflect to
Returns: (Point) The reflected point
method angle_rad(_a)
Angle in radians of a point
Namespace types: Point
Parameters:
_a (Point) : (Point) The point
Returns: (float) The angle in radians
method angle_unsigned(_a, _b)
Unsigned degree angle between 0 and +180 by given two points
Namespace types: Point
Parameters:
_a (Point) : (Point) The first point
_b (Point) : (Point) The second point
Returns: (float) The unsigned angle in degrees
method angle_signed(_a, _b)
Signed degree angle between -180 and +180 by given two points
Namespace types: Point
Parameters:
_a (Point) : (Point) The first point
_b (Point) : (Point) The second point
Returns: (float) The signed angle in degrees
method angle_360(_a, _b)
Degree angle between 0 and 360 by given two points
Namespace types: Point
Parameters:
_a (Point) : (Point) The first point
_b (Point) : (Point) The second point
Returns: (float) The angle in degrees (0-360)
method clamp(_a, _vmin, _vmax)
Restricts a point between a min and max value
Namespace types: Point
Parameters:
_a (Point) : (Point) The point to restrict
_vmin (Point) : (Point) The minimum point
_vmax (Point) : (Point) The maximum point
Returns: (Point) The restricted point
method lerp(_a, _b, _rate_of_move)
Linearly interpolates between points a and b by _rate_of_move
Namespace types: Point
Parameters:
_a (Point) : (Point) The starting point
_b (Point) : (Point) The ending point
_rate_of_move (float) : (float) The rate of movement (0-1)
Returns: (Point) The interpolated point
method slope(p1, p2)
Slope of a line between two points
Namespace types: Point
Parameters:
p1 (Point) : (Point) - The first point
p2 (Point) : (Point) - The second point
Returns: (float) - The slope of the line
method gety(self, x)
Get y-coordinate of a point on the line given its x-coordinate
Namespace types: Line
Parameters:
self (Line) : (Line) - The line
x (float) : (float) - The x-coordinate
Returns: (float) - The y-coordinate
method getx(self, y)
Get x-coordinate of a point on the line given its y-coordinate
Namespace types: Line
Parameters:
self (Line) : (Line) - The line
y (float) : (float) - The y-coordinate
Returns: (float) - The x-coordinate
method intersection(self, other)
Intersection point of two lines
Namespace types: Line
Parameters:
self (Line) : (Line) - The first line
other (Line) : (Line) - The second line
Returns: (Point) - The intersection point
method calculate_arc_point(self, b, p3)
Calculate a point on the arc defined by three points
Namespace types: Point
Parameters:
self (Point) : (Point) The starting point of the arc
b (Point) : (Point) The middle point of the arc
p3 (Point) : (Point) The end point of the arc
Returns: (Point) A point on the arc
approximate_center(point1, point2, point3)
Approximate the center of a spiral using three points
Parameters:
point1 (Point) : (Point) The first point
point2 (Point) : (Point) The second point
point3 (Point) : (Point) The third point
Returns: (Point) The approximate center point
createEdge(center, radius, angle)
Get coordinate from center by radius and angle
Parameters:
center (Point) : (Point) - The center point
radius (float) : (float) - The radius of the circle
angle (float) : (float) - The angle in degrees
Returns: (Point) - The coordinate on the circle
getGrowthFactor(p1, p2, p3)
Get growth factor of spiral point
Parameters:
p1 (Point) : (Point) - The first point
p2 (Point) : (Point) - The second point
p3 (Point) : (Point) - The third point
Returns: (float) - The growth factor
method to_chart_point(point)
Convert Point to chart.point using chart.point.from_index(safeindex(point.x), point.y)
Namespace types: Point
Parameters:
point (Point) : (Point) - The point to convert
Returns: (chart.point) - The chart.point representation of the input point
method plotline(p1, p2, col, width)
Draw a line from p1 to p2
Namespace types: Point
Parameters:
p1 (Point) : (Point) First point
p2 (Point) : (Point) Second point
col (color)
width (int)
Returns: (line) Line object
method drawlines(points, col, ignore_boundary)
Draw lines between points in an array
Namespace types: array
Parameters:
points (array) : (array) The array of points
col (color) : (color) The color of the lines
ignore_boundary (bool) : (bool) The color of the lines
method to_chart_points(points)
Draw an array of points as chart points on the chart with line.new(chartpoint1, chartpoint2, color=linecolor)
Namespace types: array
Parameters:
points (array) : (array) - The points to draw
Returns: (array) The array of chart points
polygon_area(points)
Calculate the area of a polygon defined by an array of points
Parameters:
points (array) : (array) The array of points representing the polygon vertices
Returns: (float) The area of the polygon
polygon_perimeter(points)
Calculate the perimeter of a polygon
Parameters:
points (array) : (array) Array of points defining the polygon
Returns: (float) Perimeter of the polygon
is_point_in_polygon(point, _polygon)
Check if a point is inside a polygon
Parameters:
point (Point) : (Point) The point to check
_polygon (array)
Returns: (bool) True if the point is inside the polygon, false otherwise
method perimeter(points)
Calculates the convex hull perimeter of a set of points
Namespace types: array
Parameters:
points (array) : (array) The array of points
Returns: (array) The array of points forming the convex hull perimeter
Point
A Point, can be used for vector, floating calcs, etc. Use the cp method for plots
Fields:
x (series float) : (float) The x-coordinate
y (series float) : (float) The y-coordinate
a (series float) : (float) An Angle storage spot
v (series float) : (float) A Value
Line
Line
Fields:
point (Point) : (Point) The starting point of the line
slope (series float) : (float) The slope of the line
GOMTRY.
Graphics
3D EngineHello everyone,
I am excited to share with you the first 3D engine in Pine Script! This is a remarkable achievement that will enable traders to explore the possibilities of 3D objects in their technical analysis.
To use this engine, you will need to use a higher time frame (1W or greater) to load the 3D objects in time. The code is straightforward and easy to use, with various input options to customize the object's position, rotation, and scale. You can select between two default 3D objects, Pin or Ball, by changing the 'list' input string.
The 3D engine is based on the vector and mesh data structures, and it includes several utility functions to perform operations such as rotation, translation, and scaling on these structures. It also includes functions to calculate perspective transformation for projecting 3D objects onto a 2D surface, which is the essential step in rendering the object in a 2D chart.
The 'process_scene' function is the main function that converts the 3D object data into 2D polygon data, which can be rendered on the chart. This function uses the 'process_object' function, which applies the object's transformation (position, rotation, and scale) and returns a scaled and rotated mesh that is ready for projection.
At the end of the code, there is a camera object that defines the camera's position, target, and field of view. You can customize this camera object to change the perspective of the rendered object.
To make your own 3D object, you can use the included Python program to convert an OBJ file into the format used by the engine. This program converts the OBJ file into a list of vector4 objects, which can be copy-pasted into the 'pin_vertex_list' array or a similar array. Please note that this process requires some knowledge of Python and the OBJ file format.
Overall, this is a fantastic achievement that opens up new possibilities for technical analysis in Pine Script. I encourage you to try it out and see what you can create with it.
In this code, there are several functions and data structures used to represent and manipulate 3D objects in a simple 3D engine. I will explain each function in detail below:
radians(degree): Converts an angle in degrees to radians.
quat_identity(): Returns a quaternion representing the identity rotation.
quat_from_axis_angle(axis, angle): Creates a quaternion from an axis of rotation and an angle.
quat_multiply(q1, q2): Multiplies two quaternions, q1 and q2, and returns the result.
quat_conjugate(q): Returns the conjugate of a quaternion, q.
quat_rotate(q, v): Rotates a 3D vector, v, by a quaternion, q, and returns the result.
rotate_vector_by_quaternion(v, q): Rotates a 3D vector, v, by a quaternion, q, and returns the result.
scale_vector(vector, constant): Scales a 3D vector by a constant and returns the result.
scale_mesh(mesh_obj, constant): Scales a mesh by a constant and returns the new mesh.
rotate_mesh(mesh_obj, axis, angle): Rotates a mesh around a specified axis by a given angle and returns the new mesh.
quat_translate(src, offset): Translates a 3D vector, src, by an offset and returns the result.
translate_mesh(mesh_obj, offset): Translates a mesh by an offset and returns the new mesh.
perspective_transform(msh, cam): Transforms a 3D mesh into a 2D mesh using a camera.
process_object(obj, cam): Processes a 3D object with a camera and returns a 2D mesh.
size(scene): Calculates the total number of vertices in a scene.
make_poly(scene): Converts a scene of 2D meshes into an array of polygons.
process_scene(scn, cam): Processes an entire scene of 3D objects with a camera and returns an array of polygons.
These functions work together to create a simple 3D engine that can manipulate, transform, and render 3D objects as 2D polygons. The main part of the script defines the camera, vertices, and faces for a pin object, and then uses the functions to process and render the object.
Note that some types are also defined in the code, including vector2, vector3, vector4, face, mesh, mesh2d, location, object, poly4, polyg, and camera. These types represent various mathematical structures and entities used in 3D graphics, such as vectors, faces, meshes, and cameras.
Here is an explanation of the inputs for all the functions in the given code:
radians(degree):
degree: Angle in degrees to be converted to radians.
quat_from_axis_angle(axis, angle):
axis: A vector3 object representing the axis of rotation.
angle: The angle in radians to rotate about the axis.
quat_multiply(q1, q2):
q1, q2: Two quaternion objects to be multiplied.
quat_conjugate(q):
q: A quaternion object whose conjugate is to be calculated.
quat_rotate(q, v):
q: The quaternion representing the rotation.
v: The vector3 object to be rotated.
rotate_vector_by_quaternion(v, q):
v: The vector3 object to be rotated.
q: The quaternion representing the rotation.
scale_vector(vector, constant):
vector: A vector4 object to be scaled.
constant: The scaling factor.
scale_mesh(mesh_obj, constant):
mesh_obj: A mesh object to be scaled.
constant: The scaling factor.
rotate_mesh(mesh_obj, axis, angle):
mesh_obj: A mesh object to be rotated.
axis: A vector3 object representing the axis of rotation.
angle: The angle in radians to rotate the mesh.
quat_translate(src, offset):
src: A vector4 object representing the source position.
offset: A vector3 object representing the translation offset.
translate_mesh(mesh_obj, offset):
mesh_obj: A mesh object to be translated.
offset: A vector3 object representing the translation offset.
perspective_transform(msh, cam):
msh: A mesh object to be transformed.
cam: A camera object used for the transformation.
process_object(obj, cam):
obj: An object containing a mesh and its location.
cam: A camera object used for processing the object.
make_poly(scene):
scene: An array of mesh2d objects to generate polygons from.
process_scene(scn, cam):
scn: An array of objects containing meshes and their locations.
cam: A camera object used for processing the scene.
Note that some of these functions are utility functions or internal functions, and their inputs are derived from other functions or user inputs.
I will make a library eventually.
CommonTypesMathLibrary "CommonTypesMath"
Provides a common library source for common types of useful mathematical structures.
Includes: `complex, Vector2, Vector3, Vector4, Quaternion, Segment2, Segment3, Pole, Plane, M32, M44`
complex
Representation of a Complex Number, a complex number `z` is a number in the form `z = x + yi`,
Fields:
re : Real part of the complex number.
im : Imaginary part of the complex number.
Vector2
Representation of a two dimentional vector with components `(x:float,y:float)`.
Fields:
x : Coordinate `x` of the vector.
y : Coordinate `y` of the vector.
Vector3
Representation of a three dimentional vector with components `(x:float,y:float,z:float)`.
Fields:
x : Coordinate `x` of the vector.
y : Coordinate `y` of the vector.
z : Coordinate `z` of the vector.
Vector4
Representation of a four dimentional vector with components `(x:float,y:float,z:float,w:float)`.
Fields:
x : Coordinate `x` of the vector.
y : Coordinate `y` of the vector.
z : Coordinate `z` of the vector.
w : Coordinate `w` of the vector.
Quaternion
Representation of a four dimentional vector with components `(x:float,y:float,z:float,w:float)`.
Fields:
x : Coordinate `x` of the vector.
y : Coordinate `y` of the vector.
z : Coordinate `z` of the vector.
w : Coordinate `w` of the vector, specifies the rotation component.
Segment2
Representation of a line in two dimentional space.
Fields:
origin : Origin coordinates.
target : Target coordinates.
Segment3
Representation of a line in three dimentional space.
Fields:
origin : Origin coordinates.
target : Target coordinates.
Pole
Representation of polar coordinates `(radius:float,angle:float)`.
Fields:
radius : Radius of the pole.
angle : Angle in radians of the pole.
Plane
Representation of a 3D plane.
Fields:
normal : Normal vector of the plane.
distance : Distance of the plane along its normal from the origin.
M32
Representation of a 3x2 matrix.
Fields:
m11 : First element of the first row.
m12 : Second element of the first row.
m21 : First element of the second row.
m22 : Second element of the second row.
m31 : First element of the third row.
m32 : Second element of the third row.
M44
Representation of a 4x4 matrix.
Fields:
m11 : First element of the first row.
m12 : Second element of the first row.
m13 : Third element of the first row.
m14 : fourth element of the first row.
m21 : First element of the second row.
m22 : Second element of the second row.
m23 : Third element of the second row.
m24 : fourth element of the second row.
m31 : First element of the third row.
m32 : Second element of the third row.
m33 : Third element of the third row.
m34 : fourth element of the third row.
m41 : First element of the fourth row.
m42 : Second element of the fourth row.
m43 : Third element of the fourth row.
m44 : fourth element of the fourth row.
watermark_asciiJust for fun... You can make an ascii watermark! The steps are:
1. Convert an image into ascii, e.g. using an online generator.
2. Split the ascii into strings that are no more than 4096 characters (pinescript limit).
3. Stack them together as cells on a table (as shown in the script).
I use code generation for step 2, by splitting the ascii file into chunks, then joining each line with a plus sign to make a large string concatenation statement, which I manually copy/paste into pine. Ideally, you could make this whole script into a template with a couple parameters.
Unfortunately, Pinescript doesn't use a monospaced font, so there will be some distortion. Feature request!
