3b1b-manim/manimlib/shaders/quadratic_bezier_stroke/geom.glsl

#version 330

layout (triangles) in;
layout (triangle_strip, max_vertices = 5) out;

// Needed for get_gl_Position
uniform vec2 frame_shape;
uniform vec2 pixel_shape;
uniform float focal_distance;
uniform float is_fixed_in_frame;

uniform float anti_alias_width;
uniform float flat_stroke;

//Needed for lighting
uniform vec3 light_source_position;
uniform vec3 camera_position;
uniform float joint_type;
uniform float reflectiveness;
uniform float gloss;
uniform float shadow;

in vec3 verts[3];

in float v_joint_angle[3];
in float v_stroke_width[3];
in vec4 v_color[3];

out vec4 color;
out float uv_stroke_width;
out float uv_anti_alias_width;

out float has_prev;
out float has_next;
out float bezier_degree;

out vec2 uv_coords;
out vec2 uv_b2;

// Codes for joint types
const float AUTO_JOINT = 0;
const float ROUND_JOINT = 1;
const float BEVEL_JOINT = 2;
const float MITER_JOINT = 3;
const float PI = 3.141592653;
const float DISJOINT_CONST = 404.0;


#INSERT quadratic_bezier_geometry_functions.glsl
#INSERT get_gl_Position.glsl
#INSERT get_unit_normal.glsl
#INSERT finalize_color.glsl


void create_joint(float angle, vec2 unit_tan, float buff,
                  vec2 static_c0, out vec2 changing_c0,
                  vec2 static_c1, out vec2 changing_c1){
    float shift;
    if(abs(angle) < 1e-3){
        // No joint
        shift = 0;
    }else if(joint_type == MITER_JOINT){
        shift = buff * (-1.0 - cos(angle)) / sin(angle);
    }else{
        // For a Bevel joint
        shift = buff * (1.0 - cos(angle)) / sin(angle);
    }
    changing_c0 = static_c0 - shift * unit_tan;
    changing_c1 = static_c1 + shift * unit_tan;
}


// This function is responsible for finding the corners of
// a bounding region around the bezier curve, which can be
// emitted as a triangle fan
int get_corners(
    vec2 controls[3],
    int degree,
    float stroke_widths[3],
    float angle_from_prev,
    float angle_to_next,
    out vec2 corners[5]
){
    vec2 p0 = controls[0];
    vec2 p1 = controls[1];
    vec2 p2 = controls[2];

    // Unit vectors for directions between control points
    vec2 v10 = normalize(p0 - p1);
    vec2 v12 = normalize(p2 - p1);
    vec2 v01 = -v10;
    vec2 v21 = -v12;

    vec2 p0_perp = vec2(-v01.y, v01.x);  // Pointing to the left of the curve from p0
    vec2 p2_perp = vec2(-v12.y, v12.x);  // Pointing to the left of the curve from p2

    // aaw is the added width given around the polygon for antialiasing.
    // In case the normal is faced away from (0, 0, 1), the vector to the
    // camera, this is scaled up.
    float aaw = anti_alias_width * frame_shape.y / pixel_shape.y;
    float buff0 = 0.5 * stroke_widths[0] + aaw;
    float buff2 = 0.5 * stroke_widths[2] + aaw;
    float aaw0 = (1 - has_prev) * aaw;
    float aaw2 = (1 - has_next) * aaw;

    vec2 c0 = p0 - buff0 * p0_perp + aaw0 * v10;
    vec2 c1 = p0 + buff0 * p0_perp + aaw0 * v10;
    vec2 c2 = p2 + buff2 * p2_perp + aaw2 * v12;
    vec2 c3 = p2 - buff2 * p2_perp + aaw2 * v12;

    // Account for previous and next control points
    if(has_prev > 0) create_joint(angle_from_prev, v01, buff0, c0, c0, c1, c1);
    if(has_next > 0) create_joint(angle_to_next, v21, buff2, c3, c3, c2, c2);

    // Linear case is the simplest
    if(degree == 1){
        // The order of corners should be for a triangle_strip.  Last entry is a dummy
        corners = vec2[5](c0, c1, c3, c2, vec2(0.0));
        return 4;
    }
    // Otherwise, form a pentagon around the curve
    float orientation = sign(cross2d(v01, v12));  // Positive for ccw curves
    if(orientation > 0) corners = vec2[5](c0, c1, p1, c2, c3);
    else                corners = vec2[5](c1, c0, p1, c3, c2);
    // Replace corner[2] with convex hull point accounting for stroke width
    corners[2] = corners[2] - orientation * (buff0 * p0_perp + buff2 * p2_perp);
    return 5;
}


void main() {
    if (distance(verts[0], verts[1]) == 0 && distance(verts[1], verts[2]) == 0) return;

    bezier_degree = (abs(v_joint_angle[1]) < 1e-3) ? 1.0 : 2.0;
    vec3 unit_normal = get_unit_normal(vec3[3](verts[0], verts[1], verts[2]));

    // Adjust stroke width based on distance from the camera
    float scaled_strokes[3];
    for(int i = 0; i < 3; i++){
        float sf = perspective_scale_factor(verts[i].z, focal_distance);
        if(bool(flat_stroke)){
            vec3 to_cam = normalize(vec3(0.0, 0.0, focal_distance) - verts[i]);
            sf *= abs(dot(unit_normal, to_cam));
        }
        scaled_strokes[i] = v_stroke_width[i] * sf;
    }

    // Control points are projected to the xy plane before drawing, which in turn
    // gets tranlated to a uv plane.  The z-coordinate information will be remembered
    // by what's sent out to gl_Position, and by how it affects the lighting and stroke width
    vec2 flat_controls[3];
    for(int i = 0; i < 3; i++){
        float sf = perspective_scale_factor(verts[i].z, focal_distance);
        flat_controls[i] = sf * verts[i].xy;
    }

    // If the curve is flat, put the middle control in the midpoint
    if (bezier_degree == 1.0){
        flat_controls[1] = 0.5 * (flat_controls[0] + flat_controls[2]);
    }

    // Set joint information
    float angle_from_prev = v_joint_angle[0];
    float angle_to_next = v_joint_angle[2];
    has_prev = 1.0;
    has_next = 1.0;
    if(angle_from_prev == DISJOINT_CONST){
        angle_from_prev = 0.0;
        has_prev = 0.0;
    }
    if(angle_to_next == DISJOINT_CONST){
        angle_to_next = 0.0;
        has_next = 0.0;
    }

    // Corners of a bounding region around curve
    vec2 corners[5];
    int n_corners = get_corners(
        flat_controls, int(bezier_degree), scaled_strokes,
        angle_from_prev, angle_to_next,
        corners
    );

    int index_map[5] = int[5](0, 0, 1, 2, 2);
    if(n_corners == 4) index_map[2] = 2;

    // Find uv conversion matrix
    mat3 xy_to_uv = get_xy_to_uv(flat_controls[0], flat_controls[1]);
    float scale_factor = length(flat_controls[1] - flat_controls[0]);
    uv_anti_alias_width = anti_alias_width * frame_shape.y / pixel_shape.y / scale_factor;
    uv_b2 = (xy_to_uv * vec3(flat_controls[2], 1.0)).xy;

    // Emit each corner
    for(int i = 0; i < n_corners; i++){
        uv_coords = (xy_to_uv * vec3(corners[i], 1.0)).xy;
        uv_stroke_width = scaled_strokes[index_map[i]] / scale_factor;
        // Apply some lighting to the color before sending out.
        vec3 xyz_coords = vec3(corners[i], verts[index_map[i]].z);
        color = finalize_color(
            v_color[index_map[i]],
            xyz_coords,
            unit_normal,
            light_source_position,
            camera_position,
            reflectiveness,
            gloss,
            shadow
        );
        gl_Position = vec4(
            get_gl_Position(vec3(corners[i], 0.0)).xy,
            get_gl_Position(verts[index_map[i]]).zw
        );
        EmitVertex();
    }
    EndPrimitive();
}